Compression has very little effect on the boost threshold (although not "none"), but can make a moderate difference to lag.
A higher comrpession motor is better at emptying the cylinders (more pressure at TDC for a given swept volume) and hence gives slightly more pressure in the exhaust and also allows slightly more air to be taken in on the next stroke which also means slightly more gasses for spooling.

Its not a massive effect though TBH