Yes, within certain guidelines.
The VA specifies that any non-residential use of the property must be subordinate to the residential use.
Additionally, the single family residence must be a permitted use within the way it is zoned. The county the home is in can determine this for you, and the VA will require a rebuild letter.
I am a veteran who just used a VA mortgage for a home zoned commercial low density in Brunswick county! NC. It took some extra legwork but is VERY worth it!
Suggest you look directly to the VA's website for the guidelines, as I found that the mortgage lender I used, despite claiming otherwise, was less familiar with the guidelines than I was. Also, make sure the secondary investor that they will sell the loan to accepts the zoning. My mortgage is now with Chase.