GLONASS and GPS satellite usage simultaneously by Positioning Modules
there are several things to keep in mind, when combining data from different systems.

Combining different Satellite Navigation systems

Typically it is possible to combine gps+glonass or any other navigation system. That is called GNSS (Global Navigation Satellite System). For a single GPS case you need 4 Satellites for the components [X,Y,Z, dt (the estimated receiver clock error)]. For each new systems you have to add one bias term, describing the difference between the transmitted time scales (since every system has it's own specific time scale) for each system relative to one time scale, which is kept as reference. This bias term is an additional unknown in the estimation equation to receive/determine the position solution. Consequently you need at least 3 Satellites for system 1 and 2 satellites for System 2 (for example...any other combinations are also possible). The additional bias term will describe the relative difference from one time scale to the other, (Petrowski, page 95f, 2014). 

Example: 3 GPS satellites and 2 Glonass satellites will give a direct solution without redundance (and no control). The system will be [X,Y,Z, dt(GPS), bias(GLONASS_to_GPS)]. The more satellites the more redundance is possible - and you can control your estimation process weather by RAIM, Kalman filter, least squares (sequentially) or any other processor technique.

Further details for combining different systems

Be sure to get the correct and no corrupt data from the antenna and the receiver ensemble. Since you ask if a GPS Module would be able to use GLONASS - I suggest it isn't possible, since GLONASS uses a complete different access method than GPS. GLONASS Satellites are identified by their specific frequency (Frequency Division Multiple Access - FDM) and GPS Satellites are identified by different codes (Code Division Multiple Access - CDMA). The current new GLONASS-K Satellite generation will support CDMA Signals, but the current GLONASS constellation works completely with FDMA (current GLONASS constellation)

Additionally the antenna inside the mobile device must be able to see the GLONASS-Signals to give them to the baseband processor where the GNSS signals will be aquired. Both GPS and GLONASS use different bandwiths (see signal structure in Petrowski 2014, page 39) - so you better keep in mind to use a GNSS-capable module for processing not only GPS but GLONASS, COMPASS, Galileo (and any other derivative) Data. With a GNSS receiver unit you will be able to do this, but I'm not sure if you will be able to do this with a pure GPS module.

For further reading (below others):  


Petrowski, Ivan G. (2014): GPS, GLONASS, Galileo and Beidou for Mobile Devices, iP-Solutions, Cambridge University Press, Tokyo
Hofmann-Wellenhof, Bernd, Lichtenegger, Herbert, Wasle, Elmar (2008): GNSS - Global Navigation Satellite Systems, Springer, Berlin