Some things to consider... while it probably could be done, you may not be able to get back into the suit once it's taken off. It will be SO contoured to your body that you may not be able to get your wrist through the forearm section, as an example.
It will likely tear every hair from your body when you take it off the first time. If you've ever done this over a duct tape mannequin, you run into areas where it sticks to the duct tape pretty tough, so be prepared for some pain. You're going to have to peel it off anyway, so it's going to be like a full body wax... but again, bare in mind that you're going to run into problems around the wrists and ankles when you try to peel it off.
If you do on the body, don't forget to powder it fully before trying to take it off... If you don't, as soon as you start rolling it back onto itself to remove it, you're going to have latex sticking to itself and this can cause tears or deformities.
Even though body latex cures pretty quickly, you're going to need more than one layer, as the first layer is only going to soak in and shrink... You won't get very good coverage out of the first layer and it may be even worse with body latex, as it's properties are probably a bit different than the casting latex we use, so it may take 3 or 4 layers to equal just one of the casting latex... I don't know for certain that that would be the case, but I'm guessing it would...
The fact that the first layer is going to basically shrink wrap you, you'll overheat more quickly than in a regular skin, which is overbearingly hot for some, so that would be a concern, which would also link into whether or not the latex will even cure properly with you profusely sweating underneath... Sweat will saturate the lycra, and in turn, end up "mixing" with the latex. Obviously, we cut latex with water and ammonia to thin it, but I don't know if the salt in the sweat would have an adverse affect or just the fact that the suit would be so soaked that it might not actually mix with the latex and the latex may not cure properly.
For the reasons mentioned above, I would NOT do it right on your body... BUT...
If you DO end up doing this, one thing you might consider is what I've done on an alien suit done over lycra. Now, it was still done on a duct tape mannequin, so if you do it on your body, that's up to you, but what I did was to leave maybe a 1" strip that is NOT latexed on the inseam of the legs, inner (underside) arms and sides of the top and around the waistline (if it's a 2 piece suit). These are areas that are not generally noticeable and usually black in the paint job anyway... what this does is allow at least a little stretch when putting on the suit. It made a big difference when using lycra as a base.