I still don't know if Gronk would've had a realistic shot at the ball (my actual inclination is to say no) but I will agree with the thought that there is no way that flag would've been picked up if the game was in Foxborough.
I don't think he gets to it, either, based on when he plants his right foot to cut back towards the ball and where the Panthers player goes down for the interception occurs in that gif.
I don't think he was very likely to catch it, but I'm pretty sure he would have been able to make a very credible attempt on the ball (remember, the dude is 6'7, 265 lbs). Which should be enough for the flag to stay down.
To paraphrase a former POTUS, that depends on what the definition of credible is.
It also depends on distance--how long are the letters in the CAROLINA from beginning to end of the TD zone? To my eye, Gronk plants for a cut right when his knee goes under the crossbar in that gif-what looks like more or less the horizontal division of the O.
If we assume that's his takeoff point, I'm not sure he can make it the two-ish bodylengths (looks that way to me) from that point to where the ball is intercepted by the other defender.
edit: Peyton Manning, eh? He's like geriatric at this point, right?