It really depends.
One of the stories on here I have read, and enjoy, is written by someone from Eastern Europe. I could tell even before she told someone that in the comments as the way she structured sentences wasn't how an American or British speaker generally would. Well not always technically correct, it didn't interfere with understanding the meaning, so I just ended up reading the characters voice as if they were Russian.
If however the grammar is at the level I have to reread to try to parse together what it's supposed to mean, then that is a problem. If your writing makes me feel like I'm having (another) stroke, I'll drop it mid chapter.