I generally let my troll warlock who spent years away from his tribe speak with a lighter accent when speaking orcish. Honestly, I’d prefer if more people wrote less heavy accents in general. Anyway, it’s completely possible to have someone lose their accent entirely after a while. If you study enough, you can copy a language perfectly.
Things like mouth shapes of the different races can be mostly disregarded, as tusks would give troll males a hard time pronouncing sounds common in their own laguage if we try to apply real life logic. It’s a cool world building element, but not one Warcraft seems to utilize.
As noted in earlier replies, even if your character did have an accent, you don’t need to write the accent. People can just imagine it’s there.
Basically, do what you want.