I fly an aircraft with BTMS and TPIS and on the two occasions that I’ve experienced a loss of pressure, warnings from the monitoring systems have been the only sign that anything was wrong. With two flat tyres on one side, it was difficult to tell even standing next to them.
What it would be like to run around on the rims for a while I don’t know but the rolling resistance probably wouldn’t change much (might even get less) and given that you are sitting a long way from the main gear and over the nose oleo, the harsher ride might not stand out. I recall GIG as not having the smoothest runways or taxiways at the best of times. Thinking back on it, some of the stands also had a lateral gradient, so even when parked you were not absolutely wings-level.
In situations like these, you rely on a) alerting systems, b) cabin crew noticing that it’s different from normal down the back and letting you know, c) ATC pointing it out or d) another aircraft doing the same. One would assume that none of these happened and that the flight crew were rather surprised by the state of the gear after they shut down. If they had known about the extent of the damage, I’m sure they would have come to a halt and declared an emergency.