Why not simply have an alert when you receive email from that vendor?
The browser popping up will only be useful if you happen to be sitting
at the PC with when the email arrives. An alert, on the other hand, can
fire on your cell phone, and so on.
I can think of a neat application like that to respond to auction
emails and to automatically bid on items, but it would be hard to
generalize such a feature for a wide audience. And keep it safe so that
it couldn't be hijacked to run malicious code.
If you want to open the browser to the url in the email, extract an
account number and respond to it, then you'll require some custom code.
That's why they added VBA to Outlook, to allow for all such unique
specific features.