I'd say it's almost surely impossible.
First of all, a carbocation on primary carbon is extremely unstable, so the question becomes how would you generate that. It is possible under some very extreme conditions, but then those conditions and the surroundings of the newly formed carbocation would be more controlling the reaction than the carbocation on its own. This newly generated carbocation would probably instantly react with solvent or with the leaving group thus reversing to the compound it was formed from.
Secondly, if we assume that the primary carbocation formed and this is some idealized situation where there are no other molecules around then the more probable scenario is that you will observe hydrogen transfer from the neighbouring secondary carbon, which would then undergo another hydrogen transfer, eventually forming a relatively stable tertiary carbocation.