Elon Musk's ITS proposal calls for refuelling depots order for a chemically powered transport to get around the Solar System in a halfway reasonable amount of time, so a refuelling depot in or around Mars does make sense.
For many interplanetary schemes, a refuelling depot on one of the Martian moons makes the most sense, since while you do have to slow down into Martian orbit, it is possible to aerobrake with minimum fuel and RV at the moon to take on a tank of water, or LH2 and LOX. Since Musk is interested in actually landing on Mars, his ITS proposal uses liquid Methane as the fuel, which can be created using Martian C02 in the atmosphere and bringing a small supply of Hydrogen. This is more involved, and requires you to actually land and take off from Mars itself, which has a fairly steep deltaV cost compared to pushing off from one of the moons. A well worked example of using one of the moons is here.
One reason not to go this route is the nature of orbital transfers. Synodic orbital "windows" between Earth and Mars open up roughly every 26 months, and windows to various asteroids that you are interested in visiting open even less often. Stopping at Mars then involves juggling the transfer windows from Earth to Mars, then Mars to the asteroid in question, potentially making the trip quite prolonged. If you have a powerful enough propulsion system to rapidly go from Earth to an asteroid, avoiding the synodic windows, you generally have no need to stop at Mars to refuel either (most high ISP drives like VASMIR, ion drives or even "dusty fission fragment" need very little fuel), and once you reach the asteroid belt, the odds are very good of being able to recover enough water ice to refuel on the spot.
So the short answer is going to be: no. If you are interested in going directly to an asteroid for mining or colonization, then the use of a high ISP drive eliminates the need to refuel, and also avoids the timing issues in matching synodic launch "windows" to get from place to place. Refuelling on Mars makes the most sense in terms of creating a two way transport system running between Earth and Mars (or Mars and anywhere else, for that matter).