I guess the main problem with the idea that I see (setting aside the already admitted fact that it would require a lot of rebalancing, and would most likely need to be a mod-in at this point), is that antimatter would double as fuel and as a medium for special abilities. It's sort of like that right now, but having no antimatter doesn't prevent you from travel as it would if it actually became like fuel.
If the thought behind this idea is just that it'd be cool to have a fuel/supply system in place, then perhaps it'd be better (if possible) to separate fuel from antimatter. As it is proposed, destroying the supply ships would make a little too big a dent, I think. Considering that nowhere in the grav well is safe when we have access to fighters/bombers, the fuel ships would probably be the first targets for the defending player. Then, the attacker is either forced to retreat right away, or not use any abilities to save enough antimatter for fuel/travelling purposes if he has to retreat.
If the thought behind the idea is to curb the usage of special abilities somewhat, then perhaps you could just make it so that capitals double as supply ships for their escort, recharging their antimatter stores when they are in proximity. To go along with it, the capitals themselves could borrow from EVE and treat antimatter like a capacitor with variying recharge rates based on how full they are. Too low and it recharges slowly, too high and it recharges slowly. That way the player could empty it all on specials and then spend a long time waiting to recharge, or be more moderate and keep the antimatter stores in the optimal recharge rate area.
Because this thread didn't have enough thoughts already