I opened one of these up and checked the dimensions, and the short answer is no. You won’t be able to fit a battery inside of this case. There is a small amount of extra space inside, so something like this 120mAh LiPo will physically fit, but not with enough clearance for me to be sure you wouldn’t have any heat issues or problems with battery expansion later down the line.
If you want to use this with a battery, I would suggest making or 3D printing a larger case or storing the battery externally.