Yes, it would be quite loose in there. I'd feel 100% comfortable running with it in there without a case, but I wouldn't go rock climbing with it.
This armband is intended to be used with the GS3 without a case. If I decided to go caseless and lost my current arm band, I'd buy this one without hesitation. However, I didn't recommend it directly to you because I was at work and wasn't sure how it handled excessive moisture. I just held my armband under a water faucet for 10-15 seconds letting the water run over the back of it where it contacts my arm. The back was soaked, but it didn't feel like any moisture made it into the phone's compartment.
Edit: I won't promise you that it won't fog up, but I haven't had any issues with that yet. I'm not sure if the fogging is caused by sweat wicking through the arm band or if it is due to temperature differences and humidity.
Also note that some people complain about the plastic window of the armband sticking to screen protectors. Mine sticks to my screen protector (I have a Skinomi protector, same type as a Zagg) but there's enough room in my arm band to easily manipulate it to get the phone out. I suspect that most arm bands have this issue though.