Probably, yes. "Headphone power" depends basically on two things, output voltage and headphone impedance (I discussed it in some detail here). Many devices don't bother providing a very great voltage, but for dedicated headphone amps it's pretty much expected that they can make any off-the-shelf headphones loud enough for all typical use cases.
Still, if both pairs of phones you tested are very quiet, they likely have both rather high impedance, so you may still want to try a lower-impedance pair. Or one with better isolation, so it doesn't even need to be as loud: when you're already playing an electric kit, one of the main benefits would be squandered if you then made the phones so loud that the ears suffer just as much as with an acoustic kit!