Can you soak a tampon into the betadine viginal wash?

You can, but you shouldn't.

Your vagina is self-cleaning so doesn't need any sort of product to help keep it clean - using cleaning products on the outside of your vagina, let alone inside, is unhealthy and unhygeinic as it can effect vaginal flora leading to odour and infections. Even so-called feminine washes pose risk as even if they claim to be pH balanced they cannot match your own pH.

Tampons pose high risk of TSS and vaginal infections - using tampons when not menstruating, or putting anything chemical on tampons before insertion, will increase risks of TSS and vaginal infections. This should not be done.