No, it doesn’t dramatically affect the batteries. If you’re not making many recordings, and not viewing live often, then the WiFi isn’t in use anyway. It has some effect, it’s mentioned in the above link, referenced by ceedee, but it isn’t dramatic for an infrequently used camera. More likely would be failing to work as it should, or when required.
I had one camera, an XT1, right on the brink of the possible range, but it wasn’t used very often, and never for motion. I used it every now and again for a snapshot. Batteries lasted over a year, before I changed it for an XT2, which whilst I was at it, also had new batteries. The XT1 that was there, is now near the WiFi, on the same, original, batteries, and is still going strong after 13/14 months, but it spent a year with very weak WiFi.
If it were me, I would swap the cameras around, rename them, and see if I still had a battery life issue, on the camera, even after having moved it near.
If the issue follows the camera, then it’s the camera. If the issue follows the location, then it’s the weak WiFi.