In Virginia, if a couple has a separation agreement in place and are then considered “legally separated,” can they still file married filing jointly/separately?

In Virginia, there is technically no state of being legally “separated.” You're either married or divorced. Thus you can file jointly,  separately or Head of Household if you qualify for that filing status. 

For federal taxes, the IRS does not recognize "legally separated". If you are still legally married on Dec 31 of the tax year, your only filing status options are married filing joint, married filing separate, and if one of you has a qualifying dependent then that one can file Head of Household if certain specific conditions are met.