No, that environment is not supported. I've heard of people trying, but no successes that I know of.
Yes, that's what tech support said, too. I pinged them after not receiving a response after a few days. I did learn about this resource, WineHQ which crowdsources how different Windows programs run on WINE.
When it comes to ArcGIS Pro 3.3, you can directly install it without the need to install an earlier version of Wine.
However, I have to admit that its performance is rather unstable when running under Wine.