Yes. Out-of-state drivers are no exception to Virginia’s reckless driving rules. However, there are exceptions, like
driving privileges in the home state
DMV record
Having said that Virginia can intervene and notify your home state about the reckless driving conviction, and then it is up to them to classify or not it as a punishable act.
You can, however, consult a reckless driving lawyer in Fairfax at 703-637-9999 and get legal representation despite not being the resident.