Actually that's not quite a bad idea. Of course it's only going to work for certain settings, but if you have a big enough launcher, you can impart a great deal of velocity to a missile from the very start.
I actually did a bit more of back-of-ye-fag-packet calculation. It's good for short-ranged engagements, less so for long range.
As far as throw-then-fire missiles goes, that's a nice idea - a 'drive off' launcher could work provided you can get the throw velocity high enough
In order to match the average flight speed of a 'standing start' 5g missile, you need the following muzzle velocities at the following target ranges.
short range (10km-1,250km): 0.5-5.5 km/s, average 3 km/s
medium range (1,250km-10,000km): 5.5-15.7 km/s, average 10 km/s
long range (10,000-20,000km): 15.7km/s-24.7 km/s, average 20 km/s
very long range (20,000-50,000km): 24.7-35.0 km/s, average 30 km/s
Without any real science to go on, the first two seem achievable without too much trouble in comparison to the railgun: a barbette or bay-sized railgun can fling a slug of a size not that dissimilar to a standard missile to a minimum of short range in a maximum of one turn.
Since this is the maximum range it can fire
accurately, it's probably better than this, but that's not a bad worst case estimate.
In order to cover short range (1250 Km) in 1 turn (360 s) the muzzle velocity of a railgun must be roughly 3.5 kilometres per second, which is pretty close to the short-range requirements for our 'dead-launch' missile launcher. As a result, I can imagine this sort of launch being doable to short range for a barbette/bay sized launcher if firing missiles rather than heavy missiles (i.e. about a quarter of the payload fired per turn)
A spinal launcher should easily have the accelerating barrel length to get 10 km/s, which again gives us enough heft to do the same at medium range. I'd suggest that firing any further is going to be more awkward - 20km/s or more is potentially doable but that's going to take a
very potent mass driver (i.e. one running through a multi-section capital ship).
A bigger spinal launcher isn't going to give you that much more muzzle velocity - the faster you're going, the less time you spend in that region of the barrel, hence you get rapidly diminishing returns on lengthening the accelerating barrel - but it will allow you to have multiple parallel barrels, allowing an accelerated launch of an entire missile barrage rather than a single round.
Again, this is going to be dependent on the payload of each missile and the mass of the spinal mount as to how many tubes you can fit and what muzzle velocity it can manage.
Antimatter-tipped missiles:
If you've got a ship with an AM/M reactor, then you've already got AM storage on the ship which the designers consider to be 'safe'.
Quite possibly you'd store the missiles empty, then 'charge' the missile's payload with antimatter immediately before cycling it into the launcher.