How to check protection circuit in lithium battery
If that battery has a protection circuit it will be where the leads are attached to the pouch. One of two things happens there. Either the wire is soldered directly to the pair of metal tabs that are directly connected to the battery's anode and cathode. Or they're soldered to a PCB that carries those protection circuits and is also soldered to those tabs. If you feel two largish lumps in there, it's likely to be unprotected, and if you feel a PCB with a bunch of smaller components it is likely to be protected from some situations. (You would do well to think of how to protect it from:


Overcurrent
Overvoltage
undervoltage
overtemperature
undertemperature charging


whatever protection circuit is in there might not protect the cell from those events, or might cut off the operation of the battery permanently.

More than one protection circuit there, connected through only those two wires shouldn't be a problem at all.