Given the mounting of the Alembic brass channel bridge on top of the wood riser on the first incarnations of Alligator, the action on the guitar had to be quite high. On the last version of Alligator, the wood riser was trimmed back so that it came to the edge of the bridge, but no longer ran under it. This allowed the sustain block to be installed under the bridge and flush mounted with the top of the guitar.
I believe that on the versions of Alligator prior to the sustain block, it would have been impossible to set a low action. This is an issue many of us who have built Alligators have run up against. I know of one builder that shimmed the neck to sit higher in the pocket. On my first Alligator build, I trimmed back the riser, even without a sustain block. My next one, currently in progress, will sport a sustain block.