Good question. If the BMS are designed for charging, then yes, they would terminate charge correctly. I use 12V 10ah packs, no BMS, but special 12v chargers just for that specific type of battery. Sans instruction, I don't know how you would know.
Ps, check each cells' voltage to make sure they aren't under 2.45v before charging. Those type batteries can be permanently ruined by falling too low, even once. If they're too low, they may not take a charge, and will heat up instead, eventually blowing the end out. At least, that's what a couple of mine did.
Thanks for the tip...looking at the eBay batteries, like ping for example, that come with 2-3 amp chargers for "free", I 'm thinking these are not very sophisticated units. Then again a BMS could be one that only monitors the discharge side and not the charge side, or vice versa. I'm hoping for both.
A number of threads I've read indicate a good SLA charger should work fine for the LiFePO4 with integrated BMS.