Will "hot plate" reflow soldering work without a solder resist coating?
In general, reflow soldering would work w/o solder resist.  You might get a higher incidence of solder bridges without solder resist (solder mask) than with it.

Among other things, the incidence of solder bridges depends on the pitch (spacing) between the pins of the ICs you’re using.  Fine pitch pins are easier to bridge.  For example, you’d get more solder bridges on SSOP packages with 0.025” pitch than on SOIC packages with 0.050” spacing.  What IC packages do you have on your board?