It should. I use high voltage (4.35v) batteries on my E011C builds and they work great, but you can get regular voltage (4.2v) batteries instead if that's something you're worried about. The charger that came with your F36 will only charge batteries to 4.2v anyway if you use that one. Also the F36 uses a JST PH 2.0 connector (2.0 = 2.0 millimeters between the electrical posts) just like the tiny whoop stick batteries, but they have the cable on the battery instead of on the quadcopter. So you'll still be able to use your same square batteries, but speaking from experience, the square batteries can't discharge enough current to handle upgraded motors.

If you decide to get another charger, I use this one and it has worked great for me, but some people say they don't charge to the correct voltage every time. Another good option I see recommend is the Boldclash 1S charger because it lets you set specific charging rates for each battery and has better built-in protections. Neither of these chargers come with an AC adapter. I just use my laptop charger (19.6v) on the crazepony one, but you can find adapters specifically for these chargers, like this one.