Isn't this a matter of how your server ensures the validity and longevity of logins? A server could be very picky and not allow a login to continue if it looks like it has been inactive for more than tens of seconds, or if the IP address has changed. Some servers could care less if you provide the right session or transaction ids. Then there are cookies. It would all depend on the server you are accessing.
When you say:
If so, how do you perform a check to
verify the user is logged in?
are you talking about how your iPhone app checks or how the server checks? If from the iPhone, it should try something quick like a status call and if the server requests authentication, then you authenticate. If not, server depending, you can assume you are already authenticated.
Some apps do the authentication often, assuming that the server login has timed out. Other apps don't like holding on to the user's password so they try to do it very rarely, and when they need to they display a login screen so they don't have to store the password.