I either submit tickets in game or use the for here
http://www.swtor.com/support/form to contact the via email, and usually get a quick response, so yes there is the ability to contact them via email.
From my experience there's almost no point in contacting them via email, all you're going to get is an automated reply telling you that the problem is on your end, not theirs.
Been a loyal subscriber since March last year but I've almost given up now, just waiting for the new Elder Scrolls Online game and hoping that they would do what EA-inspired Bioware failed to do with an established franchise.