I think this is one of those questions that has considerations rather than a clear answer. However, I think those considerations will usually lead one to leave the Javelin back at the patrol base.

The last time that a unit I was in carried Javelins was 2003. After that, we simply never saw any reasonable use for them. They are heavy, bulky, and pack more punch than is necessary. We did carry AT-4's, on every deployment, but not on every mission. Those are relatively heavy and bulky, but not nearly to the degree of a Javelin (and there is no $500K CLU to carry along before and after firing).

My thought has always been that if you cannot rely on indirect fire from your M203's, then you probably need to rethink your task organization or execution. (Obviously, AT-4's and M203's don't have nearly the range of a Javelin, but if the threat is that far away then how dire is the situation?)

Now, if you are conducting a mounted patrol and weight is not an issue, and you have sufficient room to bring Javelins/CLUs, then why not? Other than that situation, the negatives seem to outweigh the positives.