Cant say i've done it myself, however the free version doesnt allow HTTPS sites however the paid version does support HTTPS sites. PDAnet works awesome for me. but i never use it for banking.
They wont answer because they'll be in the legal shat if they say yes, you use it, and you get hacked.
As far as I'm concerned, HTTPS over an unsecure channel is safe enough for banking. HTTPS over a more secure channel, like the chipped channel your phone uses, is even better.
Depending on your bank, they might have an app, which would be even better.