Valve overlap is not the same thing as having the exhaust open after the transfer port closes. With overlap, the exhaust opens first, then the inlet opens, then the exhaust closes, then the inlet closes. The timing won't generally be as extreme on an engine designed for supercharge. This arrangement allows the mixture being blown in to scavenge the cylinder effectively, then after the exhaust closes it can build up pressure in the cylinder until it is higher than would usually be the case with a normally aspirated engine, giving higher power. Yes, this does also lead to higher temperatures, so there is a limit to what any given engine will stand.
With a standard two stroke arrangement, it is inherently impossible for the transfer to remain open after the exhaust closes, so you can't build up a positive pressure in the cylinder, apart from tricks with the exhaust system. Blowing will improve the scavenging and so reduce the dilution with exhaust gas that usually occurs, but at the expense of fuel economy.
John