Variacs are not isolated they are autotransformers. If you want isolation then you need the isolation transformer. As long as the thing can handle the load and is rated for your mains voltage it will be ok. I have no idea if your medical thing is suitable as you gave no information. You can in theory isolate the supply to the variac or you can isolate the variac output. Variacs take a massive magnetising surge when switched on but that won't matter as long as you have fuses to stand it.
Whether it is safe is a completely different issue. Without isolation it could never be considered safe unless in the hands of someone with enough experience to know the risks. With isolation it is no more dangerous electrically than any other device but from the non electrical point of view you must form your own opinion. To work I believe you have to hit the battery with a lot of volts. If it is badly sulphated or it develops an open circuit to the plates then you may ignite explosive gas.
I have no belief that the inductive pulse things do any desulphating, I have never tried the capacitor discharge method so I can't say if it is effective. I regard it as something for experimenters and if you are aware of what you are doing then ok. Not something to leave in the hands of an inexperienced person.
Flux