Process and Timescale
The amendment proposed by Charles Goerens was to be done to Guy Verhofstadt draft report on possible evolutions of and adjustments to the current institutional set-up of the European Union. The amendment discussion and implementation would not take long. But notice that it was only for a report document.
This kind of proposal was likely to require treaty change. There are currently two ways of revising the treaties: Ordinary revision procedure, and Simplified revision procedure. The second option cannot (a bit faster) be used to provide the EU with more powers than it has. For this reason I believe this kind of proposal to require the first option which:
... In short the ordinary revision procedure proceeds as follows: if the
majority of the European Council agrees that one or both of the
treaties require changing a Convention is convened. If the changes
needed are not drastic an intergovernmental conference is called
without a Convention. If the Convention or intergovernmental
conference reach an agreement on changes to the treaties each member
state must approve of the changes.
Unless an absolute priority this would likely take years.
The amendment never went to voting because it was withdrawn by Charles Goerens (2016) himself:
Today I decided together with Guy Verhofstadt to withdraw my amendment
on Associate EU Citizenship. We realised that this has become a very
important issue that cannot await treaty change – as was my intention
when I first tabled my amendment – since this might take years.
Yesterday evening, the House of Commons decided by a majority of
almost 400 to support Theresa May’s plan to trigger article 50 by the
end of March 2017. Hence the prospect that Article 50 will be invoked
has become very real indeed. The European Parliament will define its
position on the Brexit agreement through a resolution during spring
2017. This seems to be the best opportunity to give Brexit negotiator Guy Verhofstadt the possibility to enforce the Associate EU
Notice that even if the amendment was dropped this does not imply that the subject was forgotten. Particularly dealing with the UK citizens residing in the rest of the EU. It's speculative but this represents an ethical issue for the EU. And I very much doubt that UK citizens currently living in other member states will have big (residency) problems in the future regardless of the treatment the UK gives to EU citizens.