They will physically fit, but here is something about the focusing that is off. There are a lot of threads about this over on the rangefinder forum FSU area. A lot of people wanted to put the Jupiter 3 Sonnar 50mm f/1.5 copy on their Leicas and there is an issue with lens FFD shimming and rangefinder accuracy. There are some terrific FSU lenses out there, and they are made to work with the FSU bodies, maybe stick with that? Of course once you get your FED 1 you should screw in your Leitz lens and take some pics. Maybe it will be fine.
I have a pile of FSU stuff. If I had bought old servicable Leica gear I would probably have the same amount of money laid out on gear but it would work really well. But it wouldn't have been as much fun as mucking with the old FSU stuff.