Yep. I'm a "pro" when it comes to this bilge pump. lol Early on, there were issues with it that nobody seemed to understand. I solved them then. Point is, yes.
If you're getting the same pump, it's a very easy job. The sensor/pump side (the half towards the BOW of the boat) comes off with a simple CCW twist. You can do that now. Just unscrew that end and pull straight out. That's where all the electronics are. Leave the glue, the mounting bracket and the intake in the boat.
Make sure your battery is disconnected, then cut the the wires near the pump. Get your new pump and take out just the same part out of the box. Splice it to the same wires using waterproof butt connectors like these (Canadian link here, careful):
AIRIC Heat Shrink Butt Connectors 100pcs 22-16AWG Waterproof Butt Connector Heat Shrink Marine Automotive Electrical Straight Wire Crimp Connectors Red, Terminals & Kits - Amazon Canada
Crimp the wires, heat them to make it completely water tight, and screw the pump back into the same bracket. Done.
After reconnecting the battery to the pump, I'd recommend testing it manually with the switch, but also testing the auto pump feature. Close the drain plugs and dump some water in there until it covers the pump and it auto pumps out. Just to ensure everything is working well.
While you're down there, the intake side can be rotated and even pulled off. It's just held with an o ring. Pull the intake straight out and it will come off. Make sure there's no debris and reinstall.