It’s possible, but it’s also possible Q intentionally aged himself up to mock Jean-Luc Picard.
Q would have the power to do something like that, and doing something like that would likely piss Picard off as well.
We really don’t talk about that plot twist enough for how bizarre it is, but at least it got rid of the pesky TNG plot point.
Of course, if he really wanted to get under Picard’s skin, Q would turn himself into a Synth, seeing as Jean-Luc’s consciousness is now in a Synth body.