The MEL cannot authorize use of the GPS in Lieu of DME with an expired data base.
Advisory Circulars detail the specifics of this, but the AIM is quite accurate in it's explaination. The AIM represents a compilation of information from a variety of sources. A common misconception is that it's only advisory in nature, and this is not at all the case. Simply because something isn't spelled out in 14 CFR 91 or other parts, that doesn't mean it isn't regulatory.
Very often to get the full picture one must visit a number of sources, as each source only gives a small part of the picture. An example is owner maintenance...at least six different regulations as well as the airworthiness certificate of the airplane in question and the publications for the airplane are all applicable...far more than you'll find in Parts 43 or 91. In the case of the information contained in the AIM regarding the useage of GPS, you'll find a compilation of information which is all accurate and correct, and represents a gift to you. It saves you a great deal of reading and leg work. Rather than being suspicious of the AIM, be grateful and get to know it. It's a true and accurate representation of proceedures and policies found elsewhere.
Your MEL may authorize use of GPS in lieu of DME in the event of a DME failure above FL240. However, in order to meet this qualification, that GPS unit must have a current database. It also requires a current database for use in lieu of DME or NDB (ADF) fixes and reference during enroute and terminal operations. All approaches require a current database.
This isn't a unit specific requirement; it's universally applicable.
If you're operating under VFR, it doesn't matter...you can fly with or without a current database.
One can use a GPS unit for enroute and terminal IFR navigation with an expired data base if one verifies the information. However, one cannot engage in these operations and substitute the GPS for DME or ADF, without a current database.