If you have no legal right to possession you would technically be trespassing. However if you take possession and make it exclusive for fifteen years without being evicted it could be yours. You would have to pay taxes or lose it anyway to state. This is just a summary of how it generally works and you may want to confirm wiyh VA attorney.
Part of the concept of adverse possession is that it is not legal possession. To take title, you would need to openly, notoriously and hostilely claim possession of the property for 15 years. Paying taxes helps establish the claim and avoids forfeiture to the state. But the entry onto the property to begin with entails risk of legal action, including criminal trespass.