Is the artificial gauge field a gauge field? The so-called artificial gauge fields are actually the Berry connection. They could be $U(1)$ or $SU(N)$ which depends on the level degeneracy.
For simplicity, let's focus on $U(1)$ artificial gauge field, or artificial electromagnetic field. One can show that it is indeed gauge invariant.
My criterion for a gauge field is that it should satisfy Maxwell's equations (or Yang-Mills' equations in the non-Abelian case).
Then I doubt whether the artificial gauge field is really a gauge field.
How to write down the $F_{\mu\nu}^2$? What's the conserved current?
And can we make gapped Goldstone modes using artificial gauge fields?
 A: The Berry connection/Curvature can be formulated as the connection/curvature of a principal bundle over the parameter space, in this sense it can be thought of as a "gauge theory". It can also contain topological information, such as the first Chern number (measuring "magnetic charge"), second Chern number (measuring "instanton charge") etc., so geometrically/topologically it looks like a gauge theory.
But it is not a usual gauge field for various reasons.
First of all, the Berry connection is a "gauge field" on the parameter space and not the space-time. Secondly, the Berry phase is a purely geometrical/topological object and does not have any dynamics. So I don't think it makes sense to have a Maxwell/Yang-Mills term in the (spacetime) Lagrangian, since these terms contain the dynamical features of a gauge field. Also for this reason, I don't think it makes any sense to talk about conserved currents, etc. for the Berry connection.
It is however possible to have emergent dynamical gauge fields, but I only know about these examples in strongly interacting theories (search for example for quantum spin-liquids).
A: I believe part of your question has been answered by the paper

Simon, Barry. Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase. Phys. Rev. Lett. 51 no. 24, pp. 2167–2170 (1983). doi:10.1103/PhysRevLett.51.2167. 

Also, the gauge field only verifies the Maxwell equations without source I think, so you have $dA = F$ and that's it. Simon shows that explicitly. 
Obviously, time is badly implemented in the Berry connection structure, so there must be some trouble when trying to apply relativistic arguments. I believe there is no need for conserved current : in Berry's idea what you ('re suppose to) conserve is the ground state subspace.
I can't help you for the Goldstone mode, sorry.
