Overwatch will literally pull a decent amount of TF2 players away until the money dries up, that's if Blizzard ever let the money dry up.
Consider this like Brink v2, Brink sucked because it lacked a load of basic competitive features like first person spectating (xDDDD), but people still played it because the devs threw some money at it. Evolve even has massive prize pools because the devs throw money at the tournaments, only problem with that is you have to play Evolve.
Only thing that will threaten TF2 with Overwatch is that they have Blizzard backing it who WILL throw money at it.
The downsides for Overwatch is that Blizzard have little to no FPS experience, questionable decision making and they find ways to fuck up their own competitive formats. TF2 have Valve who have Dota2 and CSGO already thriving under a healthy matchmaking and competitive format.
tl;dr Overwatch will take TF2 players for as long as there's more money in it.