Given an adequate transformer, yes. As @dave27 indicated, if you poke around in the Video Doorbells section of the Help Center and/or check the Tech specs section on a product page of a given doorbell[1], you should see Wyze’s recommendation of a transformer with output of 16-24 V AC, ≥10 VA. My Video Doorbell v2 has performed well with a transformer rated at 16 V AC, 10 VA, though it shows me ~18.5 V AC whenever I measure it with a multimeter.
I can’t vouch for the information you say you previously received from Wyze Support and don’t know when the original Video Doorbell (v1) was released, but it’s always been wired, as far as I know. Video Doorbell Pro was released over 3 years ago and has both wired and battery-powerd configurations. Video Doorbell v2 was released last year and is wired only, and Duo Cam Doorbell was introduced several weeks ago with battery and wired power capabilities.
Now I guess you just need to decide what features you want. 
I see this for the newer doorbells but not for Video Doorbell v1 or Video Doorbell Pro. ↩︎