If it could be synthesized would it have any use?

As to the title: Cyclopropyne would, in theory, be a very high energy molecule and you would have to input a lot of energy to allow for the kind of strain that is contained in its structure. At very low temperatures you would give preference to other reaction paths that have lower activation barriers and given that the synthesis of cyclopropyne would almost certainly have a very high activation barrier, the chances of it forming would be quite low.

 

To the OP: Practically speaking, no. It would be very difficult to impossible to handle and you could presumably get similar alkylating power from other reagents.