postponing a construction credit

It is possible but not really recommended. If you postpone some credit at the Construction Preliminary submission and do not include them until your Construction Final submission, those credits would only receive one round of review. This is due to the fact that you only have one round of review left/available. If you did that and there were issues requiring clarifications, you would need to appeal to provide that information. I strongly recommend you submit any credits you wish to pursue in the Construction Preliminary to ensure that you get the two rounds of review available.

What about a design credit that is first submitted during the Final Design Review? Can comments on that design credit be answered during the Preliminary Construction Review (or would this design credit only get one review)?

Lyle,
we attempted that for one of our projects. Make sure you make a note (in the alt compliance box) that the comments will be addressed at Construction Review. We received a "Credit Denied" reply (as the de facto response), with additional advice to explain this at Construction Review submission.
So yes, it is possible;

You can also turn the design credit in as part of a typical Construction Review. Meaning you'd hold off on the initial submittal of the design credit until the Construction Review. I've done this for projects before and had success. The reviewers treat it just like they do the rest of the construction credits.