yes as long as the site is using SSL(usually url starts with https://) for the ordering process.
If your realy worried about security I would suggest getting a vpn account from some service provider to use with your touch. Good idea especially since email logins/passwords are normally transfered in the clear. I heard mail is always running touch so it would be sending out the login at random intervals. Anyone on the same public wireless network would be able to use a packet capture device if they wanted to gain access to things like that.