There would be a few issues with this approach. Firstly, back in 2012, the House of Lords Select Committee on the Constitution looked at this very argument, and concluded that even an 'opinion-poll' referendum as you suggest would require a section 30 order.
The first possible counter-argument is that if the referendum question were to ask merely for the opinion of the Scottish electorate as to whether negotiations with the UK Government should commence with a view to securing independence, then such a referendum could not of itself have any legal "effect" (within the meaning of section 29(3)) on the reserved matter of the Union. Its only effect would be to trigger inter-governmental negotiations — and to negotiate is not itself a reserved matter. There are several problems with this argument: not least that a referendum question along even these lines would "relate to" the reserved matter of the Union, especially considering that the avowed "purpose" of those proposing the referendum will be to secure a mandate to terminate the Union. Also, as we pointed out above, if the referendum question were framed in this way, this would not be sufficient to deliver independence: it would be sufficient only to deliver negotiations about independence.
Building on this last point, it might be contended that, if a referendum were incapable by itself of delivering independence, then it follows that it should not be construed as having the “effect” of relating to a reserved matter (and that it should accordingly be held to be within the legislative competence of the Scottish Parliament). This argument is seriously flawed, however, as it rests on a misapprehension as to the nature of referendums. Referendums in the UK are advisory (rather than binding) in the sense that Parliament remains sovereign: in exercising its sovereignty Parliament could legislate so as to override or ignore the result of a referendum. Whilst true as a matter of strict law, however, the fact should not be overlooked that something can be binding in the British constitutional order without it being legally required in the strictest sense. Referendums are not opinion polls: their purpose is not to test public opinion, but to make decisions. They are appeals directly to the people to make a decision that, for whatever reason, is felt to be more appropriately made by the public than by a legislature. As we observed in 2010 in our report on referendums and their place in the UK constitutional order, even where a referendum was legally only advisory, "it would be difficult for Parliament to ignore a decisive expression of public opinion".
It follows that, in our view, any referendum on Scottish independence would have both the purpose and the effect of making a decision that related to a reserved matter: namely, the Union.
This is by no means the universal viewpoint, however - writing in the Herald earlier in 2012, Professor Stephen Tierney, director of the Centre for Constitutional Law at the University of Edinburgh argued that a referendum seeking a political mandate would be permissible:
If a question is carefully crafted, asking people whether or not their preference is for independence and making clear this would only be treated by the Scottish Government as a political mandate to enter negotiations, this would seem to fall within competence. We also need to take account of section 101 which is often missed in these debates. This provides that any Act of the Scottish Parliament which could be read to be outside the powers of the Parliament is to be read as narrowly as is required for it to be within competence, if such a reading is possible. It seems it would be possible to read legislation providing for a consultative rather than a binding referendum to be within competence using a liberal interpretation as invited by section 101. But we are at the early stages of this debate and the consultation exercise issued by the Scottish Government will allow these issues to be further explored.
More recently, the Court of Session in Scotland gave the following comment in an opinion on an unsuccessful action that attempted to show the Scottish Government has the power to hold a referendum without the consent of Westminster:
The question would have been whether an Act to hold a referendum on Scottish Independence "relates to" (s 29(2)(b)) "the Union of the Kingdoms of Scotland and England" or "the Parliament of the United Kingdom" (sch 5 part I para 1(b) and (c)) having regard to its effect in all the circumstances (s 29(3)). The Act would relate to these reserved matters if it had “more than a loose or consequential connection with them” (UK Withdrawal from the
EU (Legal Continuity (Scotland) Bill 2019 SC (UKSC) at para , quoting Martin v Most 2010 SC (UKSC) 40, Lord Walker at para ). Viewed in this way, it may not be too difficult to arrive at a conclusion, but that is a matter, perhaps, for another day.
Even if we assume that after an Act of the Scottish Parliament establishing such a referendum went through the courts and was found to be lawful without a section 30 order, it would run into the same problem as the Northern Ireland border poll held in 1973. This was boycotted by Irish nationalists and led to 98.9% of votes being cast in favour of Northern Ireland remaining part of the United Kingdom. Clearly, this did not accurately reflect the opinion of the entire population - although 57.5% of the total electorate participated, there were further issues with the poll and franchise that are best described in another question. The argument could be made that should more than 50% of the whole registered electorate vote for independence, that would provide the Scottish Government with a mandate for negotiations despite a unionist boycott, however in the 2014 referendum this figure was just 37.8%; 44.7% of a 84.59% turnout.
Before it even got to that stage though, the practical matters of holding a referendum not supported by the UK Government would come into play. The overwhelming majority of local councils in Scotland have a pro-union majority, and none of the 32 councils are controlled by a single party. An unofficial referendum would be very difficult to hold without the cooperation of these councils; the entire administration would have to be organised by central government - polling stations, staff, vote counting, and so on. Furthermore, without support and regulation from the independent Electoral Commission as in 2014 (promoting public awareness, regulating campaign expenditure etc.), further questions about the impartiality of the administration of the vote would doubtless be asked. Referendums are not particularly cheap either, the 2014 referendum cost the Scottish Government £15.8 million.