If the aircraft has an FAA CofA and is not VFR-restricted (like e.g. most SE helicopters are) then it is OK for IFR if equipped accordingly and has the bi-annual pitot-static check etc.
I think the 30-day VOR check is required only if a VOR is mandatory carriage (which it isn't if you have a TSO146 IFR GPS).
However, the full equipment carriage requirements vary according to the airspace flown in and this is for all aircraft registrations. In US airspace you need a VOR, a clock, and some other stuff, DME over a certain altitude, Mode C likewise, and an IFR GPS can in some cases substitute for a DME for an IAP, etc etc. In say UK airspace, in CAS, you also need an ADF, a DME, and some other stuff, and an IFR GPS doesn't substitute for anything. In Switzerland you need an ADF for IFR in CAS but an IFR GPS gets around that. Every country has different equipment carriage requirements, which can be found in its AIP GEN 1.5.