In accord with the GLSL extension, gl_Layer in a mesh shader is part of the predefined gl_MeshPerPrimitiveNV output interface block. It seems to have the expected definition. This is a per-primitive parameter, so you can set it to a different value for each primitive you output.
Basically, yes: layered rendering is available in task/mesh shaders. And since this extension specifies the SPIR-V decorator equivalent (ie: Layer), it seems clear it can be used in the Vulkan equivalent just as well.