Welcome to the forum, granth!
Connect your ammeter across one and see what happens.
In my test, using a generic AliExpress CR2032, the current starts at 75 mA, drops to 50 mA in a couple seconds, and then settles down to 25 mA. The cell barely gets warm to the touch, even after a minute. Personally I would be more worried about component damage, but you don't have a microcontroller on board to fry ...
That said it's generally a good idea to include reverse current protection in end-user devices, particularly since you can do it with a MOSFET, which avoids the large voltage drop you'd normally get with a diode.