Does an aircraft equipment suffix denote how many VOR radios are installed?
If you look at the AIM TBL 5−1−3 Aircraft Equipment Suffixes it is split into two parts. The first part has the codes for RVSM which don’t apply to you since I presume you aren’t flying above FL 290. The second part doesn’t mention VORs at all, presumably because historically VOR and DME were almost always used together for IFR navigation. So ATC doesn’t know if you have any VORs based on your equipment suffix. However, if you use /A then they would assume you have VOR capability.

If you have a GPS installed in your plane, then you would be a /G and ATC would know that they can give you an RNAV approach. If you have a GPS installed, then you can use it in lieu of DME. The footnote to Table 1-1-6 gives the conditions when it is applicable.


  3 Requires current database or verification that the procedure has not
  been amended since the expiration of the database.


ATC wouldn’t know if your database is current, so it is up to you to accept or reject the clearance.

AOPA has a good article describing when you can use GPS in lieu of ADF and DME.

There is also a StackExchange question that discusses it as well.