Yes. If you mis-identify +Power and/or Ground, and connect them to the front board in the wrong place, you could blow the IR receiver, one of the LEDs, or possibly even something on the main board. There's also a much smaller risk that a mixup between one of the LED wires and the IR signal wire could damage the IR receiver, if its using low enough series resistor values for the LEDs.
If there's a part no. on the underneath of the IR receiver, it could be replaced, and LEDs are cheap and easy to swap, so it wouldn't necessarily be game over, but would certainly cause delays and expense. If you damage the main board its anyone's guess how hard it could be to fix - anything from replacing a single small cheap part to a complete write off requiring a new board , if its badly designed and the power supply burns up
Make the suggested measurements, and if you aren't 100% certain you've positively identified the power and ground wires don't experiment! If in any doubt, post your measurements here and wait for us to analyse them.
The safest option would be to dig into the unit enough to get decent photos of both sides of the main board, which would let us figure out the wire colours and functions from what they connect to, only leaving the possibility the LED wires might need swapping. Sure its a pain in the butt, to get to it, but you are gambling with at least $50 of boards, and that's if you are willing to wait for them to come on the slow boat from China!