Make sure you use a pan with high enough sides so that fat doesn't overflow. If it's a thin baking sheet with only short edges, especially one that tends to curve/warp in the oven, you could easily dump fat all over the bottom of the oven. But as long as it's a sturdy pan, the fat isn't going to get any higher than the beef itself started out (except for splattering), so if the beef itself all fits in with a bit of space at the top, you'll be fine. If it seems like you're cutting it close, split it into two batches.
Make sure also not to cover too tightly; you want steam to be able to escape. You want it to be covered well enough to keep fat from splattering everywhere, and to keep it from drying out fast and burning on the top or bottom, but you also don't want all the water to get stuck in there until it boils over.
Letting it cook in the fat is really just a personal preference. If you want the final result to be super lean and maybe a bit dry, don't do it; if you want to keep it moist and juicy and don't mind some fat, cooking it in the fat is good for it.
For food safety issues...
All that matters is what temperature the beef reaches. The FDA recommends that it reach 160F. You don't really need a thermometer to check in this case, though: if it's all obviously brown it's fine.
So, yes, that general idea is probably safe, but I wouldn't try to pin the time down now. Just put it in the oven and check periodically until it's done. Exactly how long it takes will depend on how thick the beef is in the pan (i.e. how big the pan is).