I can see the scenario where this might make sense, but there are a lot of "ifs" in that scenario.
#1: IF the Rams thing Robinson is the best player in the draft, and a generational talent
#2: IF the Rams think the drop-off from Robinson to every other player is huge
#3: IF the Rams think that somebody else views Robinson in the same way and is going to move up to #1 to get him.
#1 and #3 might be true, but I don't think #2 is. Even if they "miss" out on Robinson because somebody else trades up to first overall I don't think that Matthews/Clowney/Watkins/Whoever is all that bad a consolation prize. We may not get the best player in the draft, but we should still get a very good player.
However, if you're scouting staff really believes you are looking at a Manning/Leaf situation, then absolutely you trade up, regardless of what the draft pundits, media or fans think.