NO. It will not fit correctly. Before replacing it, try cleaning it.
You will need rubbing (Isopropyl) alcohol (pure as possible 100% does wonders, 90% works, too, just don't go below 90%)
iFixit guide for replacing the trackpad (sorry I can't link it, the spam filter is very aggressive here)
a toothbrush, nice soft one. medium should work, (don't go hard as you may take off the adhesive)
If you don't want to use a toothbrush, a Q-Tip should work just as well, plus, the brush may actually damage the plastic top case.
You will also need a zip-lock bag or similar resealable one that can hold liquids.
remove the trackpad from the notebook, be careful not to strip the Tri-Wing screws on the battery.
fill up the resealable bag with enough isopropyl alcohol to fully soak the trackpad (submerged, but not fully).
reseal bag and shake it a bit, but NOT TOO HARD, give it a gentle rub, etc. You want to get any debris and residue out of the touch sensors.
leave your trackpad to soak for a maximum of 2-3 minutes. use the toothbrush and rubbing alcohol to clean where the trackpad goes in the laptop, it's ok to pour isopropyl on there (as long as you don't go crazy), if you prefer, soak the toothbrush in isopropyl, just brush to get any dirt out from the top case. Inside of the case isn't required for cleaning (where the battery sits).
take the trackpad out of the bag, retaining any alcohol in the bag (DO NOT POUR IT AWAY, you may need to re-use it)
now, soak the toothbrush in isopropyl and brush around the edges of the trackpad, don't do it too hard as you risk breaking the glass or separating the adhesive.
let everything dry out for 10 minutes (just to be sure) before re-assembly.
If the trackpad still doesn't work, put it back in the alcohol. don't do it for too long, as you risk removing the adhesive holding the glass on. I think it is 5 minutes maximum. maybe 10 minutes.
Sorry if you don't understand it very well, I am doing this from memory from a youtube video I saw.
just search on YT " how to fix macbook trackpad " or something..
I am happily using an A1342 macbook and the trackpad is more rounded than one for the MBPro, so.. yeah.
This is the cheapest way and I wish you good luck with it.
if all doesn't go to plan, I am extremely sorry for it and you will probably need to buy a new A1342 trackpad from eBay (because it's way cheaper than iFixit)
All the best,