I’d worry about where the energy will come from during the cleanse. If you have plenty of fat stores you might be okay, but otherwise you might end up burning muscle. Your metabolism will also need to adjust to a low-carb diet over the first week or so, so you might be in danger of going hypoglycemic if you do any strenuous exercise. We already had somebody mentioning collapsing on the forum, although he didn’t sound at all like a sensible person.
It might be better to stick to something light, like yoga, during the cleanse and resume short jogs when you can eat some protein or generally feel up to it (I think the cleanse will take it out of you).