The answer is theoretically yes. The problem is it's a very high threshold to cross. Despite what is often said about the activism of judges, the judges in fact have exercised considerable restraint. In many situations they have taken the position that they think the particular punishment is inappropriate, but they are reluctant to say it's unconstitutional, even in particular sets of circumstances.
I think the answer has to come down to yes, it's theoretically possible to secure a constitutional exemption with the mandatory minimums, but as a practical matter it will happen so rarely that it is not worth considering as a way out.