every word in your question can change the meaning of your question. If you are asking whether we need to learn difference accents, the answer would be not. If you mean whether we should or should not speak with other students, so the answer would be positive. You need to speak with both: native and not native English speakers as much as you can.
My personal theory, as I learn Spanish, is:
--I should try to understand different national variations of Spanish, keep my ear "relaxed," try to understand local differences in vocabulary and common expressions.
--I should try to speak standard classroom Spanish. I can communicate my meaning by using standard vocabulary. Using standard vocabulary will help compensate for having an English-speaker's accent. The sound may be a little off, but it will be a word they are expecting to hear. It is only a very advanced speaker who can communicate better by choosing exactly the right idiomatic, slang, or informal phrase.
--Since I'm just "learning Spanish," not with a goal of functioning in one specific country, I don't worry too much about what kind of Spanish I am learning. I have it on good authority that Spanish speakers from different regions understand each others' Spanish, just as English speakers do.
I would ask the following, "how do you know which language you are speaking?" I carry three languages in my head and I access them by the accent, I think about the accent and then I find I can use that language. Hence the accent is vital to help me keep them apart.
Of course with English there are very many accents, so choose one that is easy to access, like "Received British".