Since I've experienced pretty decent ping (under 250) and pretty awful ping (350-900), I can tell you that your ping regardless of class is much less important in mass than in 1v1. For this reason, I only tend to 1v1 when I'm home on break aw.. but anyway.
In mass, classes you can play with fairly high ping without intense disadvantage are: Support wr, Psychic, barb, seeker, and mystic.
EA with high ping is suicidal unless you are playing with substantial support classes to alleviate enemy focus. Positioning is everything, but if your enemy is teleporting on your screen because of ping, things get tricky. For high chan ea's, you will find that your gear is being wasted because there will be a delay between skill casts, so i wouldnt play chan ea at all above a certain ping at least from a damage standpoint.
Wf and mg will have the same problem in respect to channeling your skills quickly enough in sequence to be effective.
Sin in mass as well as 1v1 is highly reactionary. You won't have much time to react if you wish to survive some aa in mass, so don't try unless you're ready to die more than necessary.
Ep in mass requires a high degree of both attention, and reaction time. Even a 2 second ping delay could cost your team a couple extra deaths. Don't be that ep who watches people 2 feet away dying and can't save them. Don't be that ep who needs an extra 5 seconds to rebuff someone either.
Sorry for any typos. I'm on my phone in a waiting room aw.