Seems to me that I didn't understand this part of the question on the 1st reading.

I see two possibilities, please try:

Option A) I would try to playback such a track, that has been recording without TM FX effects.
While playback you route the SW playback channels to a HW output (there you have FX as well like on inputs).
Now enable loopback on this HW Ouput (tool symbol, loopback button).
I never tried it but would assume that the processed signal with TM FX effects can be recorded now on the corresponding input. So if you send something out to e.g. HW output 3/4, then you should be able to record it on HW input 3/4 by loopback. Pls. try it out and report back.
You can simplify the setting work for the FX effects by using save/recall, import export functions.

Option B) An alternative solution would be to use loopback recording directly during the recording, by routing e.g. vocals to a free ADAT output, using loopback and recording the vocals track with TM FX effects in parallel / at the same time.

Option C): post #10 .. record with effects with the disadvantage, that you have the effect on the one and only recording.

Option B) would save you the work to do that later in a separate step. If it turns out, that you do not need that additional FX track in the DAW it might be quicker to delete the not required tracks from the DAW project. If your recordings are very similar, then you could even create a template which also covers the recording of these additional FX tracks.

The other question, RME FX as VST can only be answered by RME.

My guess on the subject is that the request is too specific, that would probably hardly use anyone.
On the FPGA side there are also performance limitations, more tradeoffs have to be made compared to a PC with multiple-cores. You see it already when trying to activate all FX effects on all channels on an UFX+, not possible. This shows that effects create a significant load on the extra FPGA for FX.
In addition to this everybody has already his beloved tools on PC side, be it from DAW or 3rd party. On PC side you do not have performance limitations as already mentioned. Therefore VSTs/Effects on PC side can be more elaborate and give you more options, additional oversampling and what not... So I doubt much that RME would start such an effort if the majority of customers would much likely continue use their effects or hardware effects.

IMHO you should always use the right tool for each craft. Here I see the RME FX for monitoring or vocals ideal, for which it was certainly designed. When it comes to mixing and mastering, I would recommend the tools that are designed for this use case and provide there optimal results (HW effects or more complex VSTs).