It would actually help quite a lot, especially when the gate holders are absent (Offline or fighting in other zone), if opponent will focus on them, that gate will inevitably fall, and all medals inside will be wasted, but if you could maintain green feet, attackers would not lower gate percent by even 0.7%. That will buy buildings holders enough time to come and collect fame before building is depleted.
Your scenario is strategical thinking, "Attack in Detail". Historically it was a strategy that never failed its user. So yeah, if your opponents concentrate their power while dividing yours. Surely they will make a progress, and not even Green Feet can help, but that was not the purpose behind it, it is as I stated above. Just a way to keep fame save until it is collected.
I don't see a problem if you lose a travel gate, so long that gate fame is collected. And if your opponent decides to supply it, it will only hold them back, as they are forced to divide their power to continue attack & maintain defend, or forget about it and lose all the supplies invested by a single drainer.