Seeming as the requirements to applying is 'Haven't been banned' it could be a no but there are some people that have been banned (not going to name anyone) that got to the UA rank, i suggest talking to a mod or admin about this
the answer to your question is yes u can apply but like others have said give it some more time and try be the type of player that you would want to help you. make a name for yourself as a fair helpful person and eventually the good things will outweigh anything bad u may have done in the past.