Yes, at least temporarily. In the USA, each individual state honors licenses to drive issued by sister states. This allows you to drive in states other than your home state even though you don't have a license in that particular state. For example, if your license was issued by Virginia, that license allows you to drive in every other state as long as it remains valid, assuming you have not had your privilege to drive in some other state revoked. If you have had your privilege to drive in some other state revoked, then your Virginia license allows you to drive everywhere except that state.
On the other hand, the suspension or revocation of your privilege to drive in some other state has no immediate effect on your Virginia license. In theory, word of that out-of-state suspension will be communicated to Virginia eventually and chances are good that the Virginia DMV will take some action against your Virginia license at that time. However, until such time as you are notified that the Virginia DMV has taken some action to suspend or revoke your Virginia license, it remains valid despite your privilege to drive being suspended in another state.
If you have been arrested or ticketed and accused of Driving on a Suspended or Revoked License, or some other Criminal or Traffic violation and would like to speak with a Virginia DUI / DWI Criminal & Traffic Defense Lawyer, call The Wilson Law Firm at 703-361-6100 and we'll be happy to discuss your situation with you in more detail.