No, BMSes generally do not have current limiting; except for those that shutdown the output when too much current is drawn. Some might also shutdown the input when current flow is too high, but I expect most have no shunt on the input (charging) port, only the output, so have no way to even detect this.
If yours does, then what would probably happen is the BMS would immediately shut down, and charging would not occur. Or it would shut down, then if it has a timer it would recover and restart, then shutdown, restart, etc., rather like the "hiccup mode" power supplies (PSUs) do.
If it does not, then if the voltage difference is high enough and the cells and wiring have low enough resistance, current can be high enough to cause significant heating, perhaps enough to cause melted wiring, fires from shorts if wires touch after insulation melts, cell overheating/damage/fires, etc. Or the charging FETs could be heated enough to be damaged, or to desolder themselves from the board, etc.
If you know the resistances (or can test them) you can then calculate what should happen at various voltage differences.
You'd have to test the actual situation to find out what would really happen, but I don't recommend that, unless you have money to replace anything that fails, and containment/fire suppression for the worst case results.