This depends on whether or not you are talking about African Pigmy hedgehogs
or European hedgehogs.  In the case of European hedgehogs, the answer is, of
course, yes.  In the case of the African Pigmy variety, the ones being
offered and kept as pets are now far removed from their wild ancestors.  In
parts of Europe, some African pigmy hedgehogs are still being imported, which
results in this being a more grey area.

As Nathan Tenny pointed out [3.1], the hedgehogs available as pets are a
captive-bred African species.  These have been bred in captivity for roughly
twenty years.  As such, they should not be confused with the European variety
that are wild animals (and are protected in most European countries).  It is
unlikely that a pet hedgehog could survive very long in the wild, especially
in the colder parts of North America, which seems to be where they are most
popular.  However, the chance does exist, at least in the warmer climates,
and needless to say, finding out whether or not they can is an experiment
best left to theory, rather than practice.