Yes because the unit is drawing more current, and the filament is limiting the current. However it is not "normal" to run a unit on the DBT for any more than just testing. Turn the
BIAS current down, disconnect it from the DBT, plug it into the wall directly, and adjust the BIAS current to spec. Then you can crank it all you want.
Starving any unit of current while on a DBT can be destructive. At idle, or
very low volume is fine though.