Not quite sure why it would be any different? You still select the account name as before, it's just a drop down menu instead, so you should still be able to log in multiple times.

Originally I didn't want to go this route either. It really seems that Blizzard is pushing this and will force you to go this route eventually. I was actually having problems with the regular log-in, while b.net users were not, so I figured I might as well switch and have never had a single problem. I switched about 1 month ago.

I definitely wouldn't do this if I didn't have an authenticator though.