Personally, I am leaning more towards describing lilts (like describing a French accent with soft j's or rolling r's), cursing in native tongues, and using literally translated idioms over accents, but if you want one to stick out there's no reason not to pepper it. Let's use Harry Potter as an example, Hagrid's accent is phonetically written, and the only one to do so. There's no reason not to use slang for English dialects either, like Irish using 'what's the craic?' to ask how one is or 'Grand' to say things are going well.
I think it's interesting to read, but I won't write that way myself! ETA: And on a second thought, wouldn't recommend it either. I like it when writers experiment, but it can become a chore to read after a while.
