We'll Robert April appeared in TAS' "The Counter-Clock Incident," but I don't know if STC acknowledges TAS. Phase II
apparently does given the appearance of Arex. STC might be acknowledging TAS by its inclusion of the prototype holodeck.
Since Robert April could be an Ambassador-at-large then a diplomatic type story could support his appearance. I think that would be better than a flashback, particularly if it involved scenes aboard the Enterprise.
A flashback aboard ship could involve redressing the set(s) to look Pike era. That could be problematic.
But as has been mentioned you really need the right story or it does come off as fanwank.