As the others have mentioned, it won't quite be the same ... however, it can be done, it just won't quite have the same flavor as there isn't a chance for the meat juices to transfer into the sauce, and some issues regarding mixing it back in with the cold pasta.
If I were going to try it, I'd brown the meat, remove some of the fat if it's a really fatty grind, then add some extra sauce (or even other liquid ... maybe dairy, for a classic bolognese) to let it simmer for a bit ... then toss the pasta in with it to reheat.
The extra sauce is the key, otherwise, the meat isn't going to blend in with sauce on the pasta, If you reheat the pasta in the fresh sauce, it should hopefully mix together more completely.
... but if I were to do it, and wanted to add a meat to an already cooked pasta, I'd probably not choose ground beef as a first choice; I'd probably cook up some sausages, cut it down to an appropriate size for the pasta you're dealing with, and mix that in, possibly adding some extra liquid when reheating the pasta.
Worcestershire Sauce is added where the recipe wants a fast way to develop or add savoury richness, umami.
It's often used where umami would develop over time with slow careful cooking (and heavy bottomed pans). Adding this extra ingredient is a good cheat where you just want that kick without the wait.
Best Answer
It won't be as nice if you place meat into the fresh tomato sauce.
The reason why is because you are then essentially boiling the mince, so you won't have any caramelisation happening. That caramelisation adds a good amount of flavour to the sauce, so you'll be losing that.
Sure, the mince may dry during the frying process, but remember that it will get 'rehydrated' anyway when you throw it into the sauce afterwards.
Also, by frying the mince, you render out all the fat that can be used to fry the Mirepoix to add extra flavour.
I like to add the wine to help deglaze the pot/pan once I've fried everything, then I reduce to half, then I add the tomatoes last.