By default (and most efficiently) Lightroom does not pass a rendered file to Photoshop, so to your specific question I think the answer is "does not apply". When you normally edit a raw file in photoshop from lightroom, it passes the raw file plus the accumulated lightroom edits to Photoshop's ACR, and ACR in turn converts the file internally and passes to Photoshop.

You can see if this is happening by looking at the file name at the top of photoshop when it opens - if it shows a raw file extension, it worked that way; if it shows a TIFF you are then not using the default setup, and indeed it is rendering a separate file first.

Thus to make a copy first to a local drive would actually be slower, as it needs to read the raw image only once anyway.

When your edits complete, however, it does indeed write a (usually) TIFF file back into the original directory, but that is likely what you want as you want it cataloged there. And that save can be very slow, as TIFF's are generally much larger than the original raw. But it should write the file only once.

In intake into ACR is not very fast ever, it is much slower than reading a pre-rendered file like TIFF or JPG. Because it is doing all the edits yet again, but that is not a function of NAS or not.

What may help is to follow the usual steps to speed up photoshop in general, especially where it keeps temporary files, cache files, etc. Be sure they are on fast, local disks, and you devote lots of real memory to photoshop so everything stays cached in physical memory while it is editing.

To confirm what I am suggesting, create a folder on a local drive and compare the open time there vs. NAS. It will be faster as the initial read is faster, but I bet it is not much faster. Saves, though, will be much faster for resulting 16 bit TIFF's.