Yes. Tascams can handle a hot signal directly from a SBD.
Not from their published specs, though I only have experience with the DR-680
From their published specs:
DR-680 can take +24dbu (a hot signal)
The DR-07 and DR-100 can take +6dbV max (not very hot at all)
The DR-03 and DR-05 can take only -3dbV or -4dbV --- pathetically low max input range.
Again, I haven't tried them, but I've completely stayed away from all the Tascam handhelds because of their poor stated performance for analog input. I'd never use any of those handhelds with an external preamp. Ditto for a soundboard patch if it were a DR-03 or DR-05, though the DR-07 and DR-100 are in the ballpark (but too close for comfort for me).