Now for the fun.
While some providers may not support t.38 and others not very well, t.38 is considered to be superior over a voice codec which is what the pass-thru will use.
As I stated earlier, the ISP and network in-between is the key aspect as it all about the quality and reliability of the connection such that the streams can make it from A to B with very, very little alteration.
In my area, such is hard to find and as a result, I will no longer attempt FoIP after trying almost every ATA known to man over the past 10 years. Some are certainly somewhat better than others and there is some hype with a few, but it all boils down to the delivery. If you have a good connection with decent routing thru the path, then any ATA will work.
There are a couple of providers that seemingly support t.38 well and I have used them for such without much issue, but these were sites using fiber with plenty of bandwidth headroom and in larger cities (KC, Omaha, Houston and Austin).
For my area, I use HTTPS fax or PSTN or even a EFAX type of solution. It is simply not worth the frustration and time.