It doesn't fit and it would be a little side-heavy if it did.
If you insist on a neutral LED light to fit in there, regular and tactical Quarks fit, the mini is too small and I don't have a Quark Turbo to try, but it probably doesn't since the other quarks fit at maximum capacity (held by 3-4 turns)
The HP10 can be combined with the Fenix headband so you end up with 3 good lights on your head.