Do SimpliSafe smoke detectors fit over old brackets?

Our current smoke detectors are hard-wired, so I'd just remove them and cut power, then replace them with the SimpliSafe detectors

I am not an electrician but I strongly encourage you to cap the ends of those power cables if you weren't planning on doing so.

My question is - Will they fit over already installed brackets that we have?

It will almost certainly fit over your existing brackets assuming your builder used standard mounts. (It's probably a ~4 inch round ceiling box like those found at https://www.amazon.com/old-work-ceiling-box/s?k=old+work+ceiling+box ) If you go to https://support.simplisafe.com/hc/en-us/articles/360030199891-How-do-I-install-my-SimpliSafe-Smoke-Detector- and play the video, pause around 27seconds and you'll see that the base has two slots in it to install over existing mounting screws. You can probably loosen your existing detector enough to see what the existing mount looks like and the screw placement.

Will they cover existing holes where our current smoke detectors are? 

Maybe? Probably? That really depends on how clean the mounts were installed initially. I can tell you that on my downstairs smoke detector there was some drywall damage outside the edge of the in ceiling mount and the SimpliSafe base does not fully cover it. If you don't have drywall damage or huge gaps you'll probably be fine.

Depending on where you live, it may be against fire code to only use the SimpliSafe detectors since they are neither hardwired and interconnected nor have a 10 year battery.  

https://www.kidde.com/home-safety/en/us/fire-safety/fire-safety-laws/

There’s certainly an advantage to the SimpliSafe detectors in that they are monitored, but personally, I would only install them in addition to my hardwired system. 

The smoke detectors are small and don’t completely cover the hole of the previous detector.