Should I fry mushooms before adding to a red meat sauce?
You are right on track with pre-cooking/frying the mushrooms instead of dumping them just into the dish. I think they benefit greatly from it, especially flavor-wise, which gets a lot more concentrated. Whatever you choose to do, remember that mushrooms will exude a lot of liquid during frying. 

So if you add a significant amount to your meat, it will likely interfere with the browning. The same is true if added to your vegetables from the beginning, but it won’t matter as much.

I recommend you either 


brown your meat, then add the mushrooms and use the liquid for a first „deglaze“ or
sweat your vegetables and add the mushrooms when they are like half-done.


Of course you can fry the mushrooms separately, but why bother with an extra step?