Yes, but it is not easy.
The Quantar does not contain an MDC decoder. To provide for MDC-based repeater access, Motorola adapted the so-called "SAM" card ("SAM" = Station Access Module) designed for an earlier station for use with the Quantar. The SAM is capable of decoding singletones, DTMF strings and MDC-1200 values and, upon decoding a valid tone, string or value, sending bits to the Quantar bus.
The only change you make to the Quantar itself is on the Channel Information screen, where you change the "Analog Repeater Access" parameter from "None" to "MDC/Tone." This change does two things: it causes the Quantar bus to initialize the SAM on power up, and it adds one more bit to the series of bits that most go valid to constitute "receiver qualification." The SAM provides that bit to the Quantar bus.
That's the easy part. The hard part is obtaining a SAM, installing it (it resides in the space provided for the second receiver in the Quantar cage) and programming it. In terms of programming, the SAM is the least-finished Motorola product I've ever encountered. To call it "obscure" is being kind.
There is a programming manual for the SAM. It is Motorola p/n 68P80309E35-A. As far as it goes, the instructions in this manual are correct, though only slightly less obscure than SAM programming itself. However, if you read and re-read this manual a couple of dozen times, the light will eventually come on.
If you get that far, send me a PM and I'll look around for some notes I made a few years ago on how to program a SAM for a Quantar. I like to think my notes are less obscure, but then I might be kidding myself.
There is another alternative of which I am aware, although I've never actually installed it myself. Cimarron Technologies makes a device called C Plus III, which is basically an MDC decoder/display. Per the manual, it has an option that permits it to act as a repeater access controller, essentially accessing an Aux Input on the Quantar RJ-21 connector to enable/disable the repeater based on a subscriber's sent MDC ID. The C Plus III is a superb piece of equipment, though, as I say, I've never installed one to perform repeater access control.
Info on the C Plus III:
C Plus III desktop display decoder for MDC-1200, GE Star, DTMF, Fleetsync : Cimarron Technologies for ANI Encoders and Decoders
From this page, you can download the C Plus III manual and read up on MDC repeater access control.