Before I forget,thanks to Sakwoya for writing this module. I think I answered my original question by looking a bit more at the admin settings for this module and reading Sakwoyas comments about it.
The option is in the module admin to create a customer object at Stripe. You can also enable CVV/CVC and AVS checking.
Stripe won't work unless you are connecting over SSL.
The only customer card information from Stripe pay I can find on the server is the last four digits of the card and the expiry date.