Yep, this works fine. Only limitation I found is that Strava does not import the full information from the Garmin fit-files, e.g. I cannot find left/right balance, torque effectiveness and pedal smoothness. I guess there is no solution to this until Strava change their import?
Given then number of users GC has, I really think it is for the benefit of Garmin to offer their api for free, but I understand this is not the case...