Doesn't even have to be a boutique oil, could just be a more heavily additized premium oil like Mobil 1 0W-40.
@Trav has mentioned that he stopped the notorious Honda 3.5 VCM engine ring coking problem by running a Euro 5W-40 or 0W-40 (M1 0W-40 was specifically mentioned).
Oils aren't formulated to clean (with the exception of Valvoline R&P), they are formulated to try and keep things clean enough to pass the requisite API testing. There are some base oils (AN's and esters) that are capable of actually cleaning up existing deposits, not just working to prevent them from accruing. So, depending on the severity of the issue, yes, it's quite possible that it could be mitigated by the use of a lubricant that has an active cleaning capability.
Now, if the engine has a mechanical issue, like improper heat treating or something, no, but if it's something to do with deposit build up of coke, varnish or lacquer, then yes, the choice of lubricant can in fact influence the end result.