Will a gas generator survive an EMP?
Some will, some won't. 

Most self respecting engines have electronic motor management these days, to regulate output voltage and frequency. Often you see really decent machines built into a sea container, extremely silent and the only way to tell that a generator is in them is because you're all of a sudden walking through a beam of hot air. These containers work as a Faraday cage, which in turn will probably make them insusceptible again.  

The cheap and tiny ones are often consumer stuff, they can't afford electronic management and are unstable in both voltage and frequency aswell as depending on load characteristic.

On the other hand ... it all depends on the energy contained in the EMP ... I guess you can never be really sure. Don't know if EMP is viable to melt generator windings ...