One-part putties have acetone or other solvents in them to keep them pliable in the tube, spreadable, and to make them "bite" and stick to styrene.
So yes, they will soften thin styrene.
And yes, everything should stiffen back up when the stuff dries.
For heavy fills you're really better off using a 2-part catalyzed putty.
One-part putties dry by evaporation of the solvent, so they're prone to shrinking and/or cracking if used for heavy fills.
2-part putties dry by chemical interaction, and shrink very little.