Is it legal to use GPS to navigate VOR Airways?
It's legal if you have a suitable and acceptable RNAV system as described by FAA Rules.
Also realize that it is only RNAV capability that provides for 'direct routing' without recourse to DR - Dead Reckoning - or Radar assisted DR needed by traditional Radio Aid based navigation.
When an RNAV system navigates to an out of service VOR, it is flying a computed course from it's position vis a vis the VOR to the VOR position. This is no different from flying from any point 'A' to any point 'B'. That is the whole purpose of the Advisory Circular being quoted. A few more extracts from the AC (quoted below) should make it amply clear.

FAA AC 90-108 extracts . . .



PURPOSE. This advisory circular (AC) is intended for the following purposes:



a. Provides operational and airworthiness guidance regarding the suitability and use of Area Navigation (RNAV) systems while operating on, or transitioning to, conventional, i.e., non-RNAV, routes and procedures within the U.S. National Airspace System (NAS). This guidance material applies to two broad categories:



(1) Use of a suitable RNAV system as a Substitute Means of Navigation when a very high frequency (VHF) omni-directional range (VOR), distance measuring equipment (DME), Tactical Air Navigation (TACAN), VOR/TACAN (VORTAC), VOR/DME, non-directional radio beacon (NDB), or compass locator facility including Locator Outer Marker (LOM) and Locator Middle Marker (LMM) is out-of-service, i.e., the Navigation Aid (NAVAID) information is not available; an aircraft is not equipped with an automatic direction finder (ADF) or DME; or the installed ADF or DME on an aircraft is not operational. For example, if equipped with a suitable RNAV system, a pilot may hold over an out-of-service NDB.




(2) Use of a suitable RNAV system as an Alternate Means of Navigation when a VOR, DME, VORTAC, VOR/DME, TACAN, NDB, or compass locator facility including LOM and LMM is operational, and the respective aircraft is equipped with operational navigation equipment that is compatible with conventional NAVAIDs. For example, if equipped with a suitable RNAV system, a pilot may fly a procedure or route based on operational VOR using that RNAV system without monitoring the VOR.



b. Qualified RNAV Systems. Describes the types of RNAV systems that qualify as “suitable RNAV systems”



DEFINITIONS. For the purposes of this AC, the following definitions are provided:



b. Area Navigation (RNAV). A method of navigation which permits aircraft operation on any desired flightpath within the coverage of ground- or space-based navigation aids or within the limits of the capability of self-contained aids, or a combination of these.


g. Substitute Means of Navigation. The use of information from an RNAV system in lieu of that from out-of-service conventional NAVAIDs and/or inoperative or not-installed navigation equipment compatible with conventional NAVAIDs.