You can, as long as certain conditions are met. You need to know the starting current of the engine, and confirm the BMS can handle it. Usually that means a BMS with contactors. The cells themselves need to be able to handle the current. Assuming a 1C max rate, 280 is pretty small, but might work for a smaller engine. You could parallel them for 560Ah.
Lastly, LiFePO4 does not like to be held at full charge, and most starting batteries are always at 100%. OTOH, Lead batteries prefer to be held at full charge. So a lead battery could see as long of a life as LFP in a starting application.
However, I know of some installations where there was no separate starting battery, the house battery served both functions. They were large ~1000Ah, had contactors, and because they were used for house loads were not often at 100%. After many years (>10) they still work great.
Re: the alternator. Not really related to staring applications, as Alternators often charge house batteries also. The best solution is an externally regulated alternator with a regulator that has an LFP charge profile. This allows the alternator to run at max safe current, protected by a temperature sensor on the alternator, and charges the LFP at the correct rate/profile.