is it a system limitation, or can this be made to work with triplanar mapping?

Triplanar is something that is defined by the material, thus it doesn't affect vertex coloring. It works the same way as if you didn't have triplanar mapping.

Example in Godot:

• Mesh with StandardMaterial3D,  check "Vertex Color: Use as Albedo"
• Assign a texture
• Check Triplanar in UV1
• Save and re-open the mesh scene if needed
• In Vertex Studio, click to restore the Original Material, painting work as normal, but to see the triplanar mapping you have to keep using your mesh's Original Material that has the "Triplanar" setting as on, as shown in the second screenshot below (you can click the arrow icon as many times as you want/need).