I mentioned this in another thread that talked about accents, and what can happen when native speakers are performing their "accent" in a second language.
It's actually very difficult, and it's not always the native speakers who manage it most consistently. But it varies.
Leli's accent definitely wavers, coming and going depending on the scene. Strangely, I find it a lot more noticeable in DA:I than I did in DA:O.
Then you have Lambert Wilson, who speaks flawless English as a second language, and he was "faking" his French accent throughout the Matrix trilogy, despite being a native French speaker. His accent was extraordinarily consistent in the trilogy, not wavering at all.
Sometimes non-native speakers can manage amazing accents, even if they don't understand a word that they're saying. Ron Perlman is famous for this. He didn't understand a word of his dialogue in the movies In the Name of the Rose, or City of Lost Children, but his accents in both films were incredibly consistent (he learned his lines phonetically.)
I guess, in the end, it really comes down to the actor, more than whether they are a native speaker. Fundamentally, their job is acting, which includes putting on an accent in some cases. People who have a skill for it will do it better, in many cases regardless of what their native language is.