Will Strava iPhone app work on t-mobile 2g/edge?

Right now t-mobile only offers 2g/EDGE data speeds for unlocked iPhones brought to them. Is that fast enough to use the cycling app Strava?

I'm not 100% sure but am fairly certain that the Strava App works off the GPS sginal and not the mobile network. - As long as your phone has GPS there's no reason it will not work.
You should note however that phone gps is not as good as a bespoke devices so if you want best quality data you should think about investing in a Garmin or similar.