add the word "significant" to your theory and there you have the answer.
beside the fact that every kind of interaction in the entire universe has an effect of some kind, while it remains to determine which and where, i think if you add the word significant to the word effect the answer is clearly "NO" it might have an effect like everything else has, but which effect that is and where it does apply is somehow of low relevance as long as the effect is not "significant" which i think is quite obvious considering the levels of energy needed to affect polar ice caps in general.
however, i still like the question and any discussion on such topics because however things are on the topic, there is usually something to learn for everyone who is not active directly in the field of science in question.
don't hesitate to continue and bring up further arguments and stuff, i'll read, consider and filter with pleasure and should by any means the discussion here end, there always remains PM for a further exchange.
plus what jim said