Any scene containing CGI would still be SD, although if it isn't cropped from 4:3 to 16:9, the amount of blurriness should be reduced. However, I can't see Amazon stumping up the cash for this if they don't think the return on their investment will be worthwhile. Warners might just flat out say no, of course.
According to JMS, who was the producer of the show, at the end of each season each episode was reprinted to the broadcast cuts on a new negative reel, with the CGI rendered directly to film and comped into the negs automatically ("i.e. a conformed cut").The CGI wasn't even done in progressive. It was done in 480 interlace. So any film transfers would've been from 480i tapes.
This would mean that there is a 4:3 SD print of the show on 35mm negatives, which can be upscaled to HD fairly easily with very little loss of fidelity. Since these reels are already conformed and are essentially 35mm backups of the show as it aired, they can be transferred and upscaled for dirt cheap.
The current transfers in existence were scanned from the telecine or laserdiscs, which means broadcast quality.