You should still be able to connect to the network with a non-T-Mobile device. Are you getting an error message when you attempt to search for the T-Mobile network? Is the issue specific to a location? What device/bands are you using?
Hope to hear from you soon!
There are some (really old) phones in Europe which do not support the GSM bands in North America at all, they support only 900/1800.
T-Mobile has the GSM 1900 network. (and 850 would be the other network in North America for GSM)
T-Mobile also supports the UMTS band called AWS, or 1700/2100 or Band IV
As a user you would not have to do anything to have it select the North American bands (this is not true for older phones where you have to change the bands in the System selection menu).
Your SIM takes care of what network you can register with (assuming your phone supports the band)