Hi ElvisQ,
I think not, unless there's some significant voltage regulator in the battery adapter. The Quantum (nice Q connection in the name at least
) batteries are meant for flashes that use 4-5 AA batteries, so 6-7.5 volts. The Q battery is 3.5V.
A possibly more practical solution would possibly be a battery grip that attached to the body and used 2 AAA or AA batteries, which would give you @ 3V. I don't know if this might be enough to power the Q effectively, but I think it might. I'm not a fan of the battery grips for DSLRs, but I'd actually like something that might extend the right side of the body out a little further for use with adapted lenses. With an adapter mounted, especially the Pentax OEM, there's very little to grab on the right side of the body. . . and of course, more battery capacity would always be welcomed with the Q.
Scott