Absolutely!  Assuming you are over 25, a reasonable rental is easier to
find than you might imagine.  Particularly lf you want to try a late C5
rather than a C6.  Google for <corvette rentals> then call local limo
rental firms and ask who rents corvettes.  Do some shopping for price
versus days of the week.  Let them suggest a date or ask them to call
you when they've got a spare car for a couple of days.  Have insurance
records handy. (Usually won't make a difference but one local exotics
outfit trades a good-driver-discount on the policy or a printout of a
clean driving record for not lodging a hefty reserve against your credit
card.)

For several years I rented C5s for business runs to Las Vegas.  Got to
know the folks up front.  Taking the car late Monday morning and
returning early Friday was less than 1/2 the rent-a-vette rate.  Finally
replaced a business lease with my C4 and bought my own C5 for weekends.

Consider renting both an auto and a manual. A Z06 will usually go for a
 premium.  Fun car but in my (NSH) opinion, it's not worth it for just
an intro ride.  A C5 or C6 base coupe or convertible will tell you what
you want to know.  If the want the extra bite and kick in the fanny then
buy a Z06.

Renting also reveals a few things about Corvette sturdiness.  Most of
these cars have seen more than their fair share of 1/8 mile challenges
and physical abuse from customers that don't know how to get into and
out of a Corvette.