Not without DM houseruling
Spells and items do what they say, and Long Rests and Short Rests are separate activities.
This boon resets only a Short Rest. If it reset on a Long Rest, then it would state "Short or Long Rest".
In fact, Jeremy Crawford went out of his way to differentiate Short and Long Rest mechanics:
Short and long rests have different places in the game's narrative, as described in sentence 3 of "Resting" (PH, 186).
Many features are refreshed by a short or long rest. If a long rest included a short rest (it doesn't), such features would refer only to a short rest.
But will it really matter?
Probably not, but adding an extra hour either before or after a long rest isn't a big deal, either. Up to your table and DM as to whether or not (or how) you meld those rest mechanics.