Yes, it is possible to remove it as a whole unit. I did that on my 1931 model # 608 QC gearbox awhile back as part of the commencement of a general refurb. I had knocked a lot of the lathe down at that time for various reasons.
Reassembly was undertaken only a month ago and proved more difficult however. The problem was the side of the gearbox unit was not going all way to bed of lathe…I was coming up about 1/2" short of mating. At first I thought it was an issue with aligning 2 pins that needed to mate in the blind hole.
The instructions I found in the vintage Rivett materials online suggested the re-attachment would be uneventful (see attached). It was proving to be quite frustrating.
I decided to take it further apart. I wanted to lube the QC gears and see inside there anyway. I broke down the gearbox by my own deduction, pulling the unit apart and exposing the set of QC gears.
When I went to put it back together I encountered the same problem...except I ruled out it being an issue with the alignment pins. It was a press fit and would not go on so I heated it with the heat gun and then using gloves and a deep socket as a drive collar I lined it up with the pins and hammered it into place quickly after it had expanded. Then I reinstalled the gearbox housing back into place.
So it is back on and I have moved on to other aspects of the refurb...it has not been fully tested (but I was)
If you would like to PM me I have more photos and further explanation, etc. of what I've just described..you show me yours and I'll show you mine via email, which is the route I'd prefer.