Can I use a generator with a bonded neutral with my interlock switch?
For a GFCI to function properly there cannot be a parallel path on the neutral conductor.  By using a GFCI compliant transfer switch, it disconnects the neutral conductor too thus preventing a parallel path.  It's a great design to incorporate this extra layer of protection for small portable generators.  

Now if you're using a permanently installed generator that is hard-wired you have the option to chose whether to switch the neutral or not.  This is technically referred to as separately derived vs non-separately derived and all depends on the particular design setup.

There are advantages to each. One being non-separately derived systems do not require extra ground rods which has a tendency to let lightning back up into the structure damaging electronics.  More ground rods do not equal better protection.  It can actually cause the opposite to happen.  

But again, small portable generators that are not designed to be hard-wired are unique in that they can be separately derived and still not require a extra ground rod as they are portable and not permanently installed.