While Warlock slots refresh every short rest, this wouldn't change how the Pearl or Gem worked. (A Pearl could still only be used once until next dawn. A Gem can only be refilled or "imbued" once until next dawn.)
It's not like the pearl gives the Warlock a new, third, spell slot, that takes on life of its own (starts to recharge every short rest).
A pearl can be used once per day to restore a Warlock's spell slot between short rests.
A gem can be used during the day, then imbued, then used again that same day. (But that only holds true for the first of a series of days: on the second and every subsequent day, you can imbue it and use it once)
Apologies if this wasn't what you were talking about.
