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There's really no reason to believe that a lighter Boxster with a turbo 4 couldn't outrun the current car, even the S.
If it went from 3000 pounds to 2600, 13% less weight, it would need 13% less torque to get the same acceleration. This is why the Elise only needs 200hp to do 0-60 in 4.5 seconds.
Even if the weight didn't change, 310-320 hp isn't a challenge for a turbo 4. In fact, that's about the output of the flat-4 in the Impreza STI. When you add direct injection to a turbocharged engine, you end up with a drivetrain that hasn't sacrificed drive ability at all. Compression can still be relatively high, meaning off-boost torque is high and turbo lag would be minimal. If you've ever driven a well sorted turbo 4, you'll know what I mean when I say the torque wave can be addictive. It's a feeling the current NA engines don't have.
The advantage to having an engine designed for forced induction from the factory is that it has to be more robust in the first place. Adding higher boost and more fuel is a cheap proposition to adding more power as compared to where we are in the current car.
The other advantage to using a DI turbo 4 is in fuel economy. It's easy to drive a turbo car without spinning the turbo much as turbo activity is related to load and speed combined. If you drive gently, you can greatly increase fuel economy compared to a large engine of equal power.
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