If coast guard ships were to be drafted into navy combat duties in war time, most likely they will be equiped for similar roles of type 056 and type 056A, i.e. coastal patrol and shallow water ASW roles. I don't foresee that they will be deploy for anti-ship roles, thus won't be fitted with any long range anti-ship missiles.
What role that will be given will depend on the displacement of each ship, since CCG possess ships and boats below 200 tons to that above 10,000 tons.
It is also very unlikely those large ships will be retrofitted with any air defense missiles, nor any VLS. The time to refit CCG ships to navy standard may not be much shorted than building a new navy ships like type 054A. The refit of CCG ships requires more than just add a few missiles launcher racks and a fire control radar. There will be systems integration among all electronic suites, re-positioning of sensors to avoid electronic signal interference, re-training of the crew etc etc.
It would be better just to produce more dedicated warships rather than spending time and money on refitting CCG ships to carry anti-ship or air defence missiles to the level of type 054A or beyond..
That seems to be the most plausible way to bring the CG ships into service actually, as auxiliary submarine chasers, which can be an impactful function. What this would take is to install naval sonars, including the stern mounted TASS and VDS, which would be feasible for ships of a small tonnage that is not designed to do anything else. The contributions would be from having more detectors in the water. Actual ASW firepower could come from real warships.
Edit: I'll just add that the Russian Navy is using the coastal ASW function to give extended service life to many of their would-be obsolete Soviet-era warships, espcially the small ships such as the frigates and corvettes. The Grisha class and Parchim class corvettes are retained to serve the ASW role, whereas otherwise they would have been retired five years ago. Same with the Krivak and Neustrashimmy class frigates. They have virtually no AsuW and only self air defence, but the Russians are happy with how they are being used.
Another role for CG ships could be auxiliary mine countermeasure vessels. They can be fitted with special sonars, and stern-mounted mine neutralisation systems to trigger bottom-dwelling mines. I don't know how much this would cost, but there's enough space on small ships to do this. If space is limited, they can focus on acquostic or magnetic mine triggers only. There's plenty of chokepoints in the Western Pacific that cna be blocked with naval mines, so this is a useful role.
Fitting anti-ship missiles into CG ships would take a lot of time and resources that would be better spent on finishing the fitting out of any launched warships, in a war contingency. ASCMs by themselves are not useful without fire control radars and good search radars. Air defence (except self defence) would require an even greater level of investment, with VLS cells, 3D air search radars and C&D systems.