I don't believe the Corvette came with a supercharger, so this is
something the last owner added and the car may or may not comply with
emissions standards in your state.  Surging idle isn't normal and may
be indicative of an easily solved problem or botched supercharger
installation or something else.

If you are interested in the car I would get it thoroughly checked out
by a mechanic who is familiar with vettes.

it might be normal for that install, but it's not normal for a properly
set up supercharger install.  All those Pontiac Bonnevilles with the
'charged 3.8 idle pretty tamely.

And no stock 03 Vette comes supercharged, so I'd consider getting an
independent mechanic assess the install and the rest of the
powertrain... the stock LS1 clutches don't hold up to power adders that
well, and well... if it's been raced, it should be priced accordingly.

There's nothing wrong with a modified car - I have nitrous on my Trans
Am, but buying a used modified car is always a bit of a crapshoot... is
this engine #2, transmission #4 and rearend #3 because parts keep
breaking?  Or does it overheat all the time and fail emissions testing?
 Why is it being sold?

The fuel mixture control is probably part of the SC kit - what does the
owner say about this?

Ray

The surging idle is not something to just glance over.  I have a
supercharger on my 89 Trans Am and the idle is steady.  There is definitely
something wrong.  Probably a vacuum leak possibly caused by going into boost
and blowing a vacuum line off that couldn't handle the added pressure.

The fuel/mixture control is meant to keep the air/fuel ratio rich when you
go into boost.  If you lean the mixture out too much, you will burn a valve
and you'll experience more problems than you already have.  To set it, you
need to know a lot of information you'll probably never get.  Typically one
would overly richen the mixture and slowly work down from there until the
air/fuel ratio gauge shows the mixture registers on the scale instead of so
rich, it's off the scale.