Yes, yes it will. (Well, at least it should. If it doesn't, that's a bug.)
The problem here is that the premise of this post is evaluating buying a GPU with AV1 encoder in order to transcode a media library. Any GPU-based AV1 encoder will produce very different results than svt-av1, likely much worse results that is.
Yes, a slight speed decrease is expected even with good proxy services at common residential speeds. Given that yours is far above the average, a greater decrease can be expected. It shouldn't be this much though.
If this is installed on a common "router" SOHO gateway appliance, it's likely that its hardware is simply not able to keep up with the tunnelling workload (encryption, package handling). For troubleshooting, try the same proxy server on a more powerful machine while disabling the proxy on the gateway. If it's faster, that's likely your issue.
Also try a different proxy server. That particular one might simply not have enough capacity to serve you more than that.