I don't see why not. I certainly plan to, though as people have pointed out already, you will have to make adjustments. E.g., I usually work with (heavy) dumbells. Obviously, that won't be possible. You would have to use machines mostly, to avoid putting excessive loads onto your legs. Think shoulder press machine, pecs machine. Back should be easier. Lat pull requires your legs for balance, but if you have a weight bearing nail, that should be fine. Maybe the same for cable rows (depending on how heavy you want to go). Pull up bars will be fine and probably the best way to build your back.
What I can say is that you can workout during lengthening, as I am doing it. The best way to do that is using resistance bands. Not only am I allowed, but my doctor and physios even required me to work on my upper body with dumbells, though of course their idea of working out was using very light dumbells (few kgs). That is because you will need upper body strength during lengthening, as you will be relying mostly on it, especially in the beginning. Depending on your fitness level, light dumbells might be enough. But if you want to work out moderately heavily, the bands are the way to go. You can pick a heavy resistance band and work on your chest, shoulders, arms and back. If you search for Youtube videos of wheelchair exercises with resistance bands, you will find plenty.
Now, if you were lifting heavy weights at the gym before, be under no illusion that you won't be able to keep up the same level of intensity (you will lose some muscle mass) but it's still better than doing nothing. Personally, I can tell you the difference between my legs and upper body now, one month into lengthening, is night and day (think Johnny Bravo). My legs have turned into sticks, but thanks to my upper body workouts plus the fact that I have to use my upper body a lot more to compensate for the state of my legs, I am still maintaining a fair degree of upper body muscle mass.
Best of luck with your journey.