As there is no precedent, we cannot definitively answer the question.
However, it seems that the distinction between "Members" and "Members-elect" of the House of Representatives does not matter as far as certifying the results of a presidential election is concerned. Thus, I think that, if the situation arose, the count on January 6 would likely proceed as normal without a Speaker.
Let's look at the basis for the distinction between Members and Members-elect:
The Rules of the House of Representatives (page 163) has the following to say on the matter.
The status of a Member-elect under the Constitution undoubtedly differs greatly from the status of a Member-elect under the law of
Parliament. In various inquiries by committees of the House this question
has been examined, with the conclusions that a Member-elect becomes
a Member from the very beginning of the term to which elected
In terms of swearing in Members, 2 U.S.C. § 25 says
At the first session of Congress after every general election of Representatives, the oath of office shall be administered by any Member of the House of Representatives to the Speaker; and by the Speaker to all the Members and Delegates present, and to the Clerk, previous to entering on any other business; and to the Members and Delegates who afterward appear, previous to their taking their seats.
If we are to accept that Members-elect are not Members, then this statute makes no sense: How can a Member of the House of Representatives administer the oath of office to the Speaker if there are no Members prior to the Speaker swearing them in?
The 20th Amendment is pretty clear too:
The terms of the President and Vice President shall end at noon on the 20th day of January, and the terms of Senators and Representatives at noon on the 3d day of January, of the years in which such terms would have ended if this article had not been ratified; and the terms of their successors shall then begin.
In particular, it does not say that the terms of Representatives begin after they are sworn in.
Thus it seems that the distinction between Members and Members-elect is not material to the Electoral Count Act which governs the certification of Presidential election results.
The Electoral Count Act stipluates that, when the two houses of Congress meet on January 6, "the President of the Senate shall be their presiding officer" -- i.e., the outgoing Vice President presides, not the Speaker.
The only role for the Speaker under the Electoral Count Act is in handling objections:
When all objections so made to any vote or paper from a State shall have been received and read, the Senate shall thereupon withdraw, and such objections shall be submitted to the Senate for its decision; and the Speaker of the House of Representatives shall, in like manner, submit such objections to the House of Representatives for its decision
If no objections are raised, then this is not a problem, but it becomes unclear what happens if objections are raised.
Interestingly, the Electoral Count Act was amended last week and it added the following requirements for objections to be considered:
No objection or other question arising in the matter shall be in order unless the objection or question ... is signed by at least one-fifth of the Senators duly chosen and sworn and one-fifth of the Members of the House of Representatives duly chosen and sworn
If no Members of the House of Representatives have been sworn in, it seems they cannot sign an objection. If that means no objections can be considered, then the role of the Speaker is moot! (Although this last point is potentially unclear. It could also be interpreted that if no Members have been sworn in then one-fifth of zero is zero, so no Members are required to support an objection.)
Aside: Until the early 20th century, the Speaker of the House of Representatives was elected before the start of the congressional term. Thus, historically, the votes for Speaker were indeed cast by Members-elect who were truly not yet Members. I suspect that the current usage of the term "Member-elect" to refer to current Members is a legacy of this historical practice, rather than a meaningful legal distinction.