What Adam said.
A few years ago I tried to force a wet sheet transfer to prove the point.
Soaked well, placed inside folded paper for a few days in a vise 2-5 tons of pressure.
The paper got a nice card shaped embossing, and both got a woodgrain embossing that doesn't show in the scans.
No transfer at all.
Soaking in solvents might do it, but I haven't tried that. And probably won't.
The card is a fairly worn common, and the embossing may have worked its way out. I'd have to find it and check.
The exact formula for the ink will be important. Some of the bases used harden and simply won't transfer. Others dry, but never completely, and with pressure and vibration might transfer, but not all that clearly.