You will, or can, get quite close duplicate prints with burning, dodging and the like, but not really duplicate in the sense of the word.
You can do a copy negative, but realistically it should be a flat, or low contrast negative of a good print.
From there you should be able do reasonable copies of your original dodged and burnt print, not duplicates, but quite close.
How acceptable this is, is for you to judge, but if you have to do multiple prints, then this is a possible viable proposition.
Last year I had a job of doing around 3,000 prints from the same negative. I made a master print which the client approved. This was from a 35mm negative.
I then used a 4x5" camera to make a copy negative, actually 4 negatives with various exposures, developed the lot in one hit and found the best negative that would reproduce a straight print with a reasonable closeness to the original print.
Checked with the customer the go ahead was given then I hit the darkroom.
Enlarger globes going off have to be monitored by having at least a couple of master prints nearby.
You should think about comparing every 30 or so prints with your master print to ensure you are still on track, it really is easy to slowly wander and not realise the prints are too light, dark or lacking in contrast as the developer goes off.
Assume a contrast increase with any copy negative. This is usually looked after by making a slightly flatter print to copy.
Mick.