If its just an AC starting, the breaker(s) should be able to deal with that startup time. That 100 amp breaker will notice the extra 20 amps of AC startup draw than the smaller individual breaker driving the AC.
But it could be >much< worse than that, in theory. There could be some subset of loads that run at 90 amps for one minute, then they go away and you use 20 amps for the rest of the hour. If you add even 24 amps to that load, you might see 'correct' tripping action on the main.
If you have a clip-on ammeter, you can actually measure the current flow through your main wires in real time(gotta take the cover off the panel and know what not to touch in there to do it!). If you are REALLY interested, there are some really neat products that will do that in real time and remotely(Efergy is one, Sense is another, EnergyCloud is a third... the list goes on). Efergy's and Sense's products are full-time clamped onto the supply cables in the panel, EnergyCloud clamps onto the outside electric meter itself and physically reads the spinning disk..... I've found the outdoor meter reader part of this to fail after two years, which sucks, but maybe they've improved it.)
Even if you don't have a clip-on ammeter and don't want to get one of the above, you should be able to do a decent job of checking the power flow just using the electric meter. Some digital ones will actually display real-time power usage, if you have the spinning disk type, you could count the spins-per-minute of the disk and then do the math... sadly there doesn't seem to be a 'standard' for the spins per kwh...
Electricity meter - Wikipedia ... but it isn't hard to figure out....
Your AC isn't the only load in your house by any means... Imagine you are doing some clothes drying while cooking your Thanksgiving turkey and your refrigerator decides its time to defrost, and the hot water heater is heating water because you just cooked or took a shower and your 3 is out in the garage drawing 48 amps because you just gotta drive over to grandma's house after the turkey is done.... its unlikely, but also perhaps the worst time to have a nuisance trip of your main.