Your DC/DC converter will be safe as long as the battery is in-circuit, but you may mess up your battery charging. If your BMS open-circuits the connection to the battery your system as a whole probably won't work, but as it's malfunctioning the charger will probably hold its output to what it thinks a battery pack should have.
That converter will put a load on the battery pack. In general, the load won't mess up the gross behavior of the charger, but it will mess up charge tracking and termination. This is because the charger will not be able to properly account for how much charge is actually going into the battery
The CC mode of charger is there for one of two reasons: to hold the current going into the battery to protect the battery, or to hold the power level of the charger down to protect the charger. You decide how much you want to spend on the charger and you choose. Any current going into your load is going to be stolen from the battery; if it isn't measured at the battery, the charger will not be able to properly track the amount of charge going into the battery.
The most basic way of implementing charge termination on a Li-whatever pack is to monitor the current in CV mode, and terminate charge when the current has dropped below some threshold. Again, with your load, the charger will see the combined battery + load current as just the battery current, and it will never terminate charging.
I don't know your system constraints, but I think your best bet is to look for a charger/BMS combination that's designed to handle exactly this situation (there's chips out there to do it in smaller systems; there have to be modules out there, too).