Prior to launch, that wouldn't happen. AFAIK, most current designs only align the detonator after launch, and the detonator being set off before that would not launch the main explosive train. You'd only get a broken detonator. The detonators on most missiles are also buried deep within the missile itself, usually imbedded in the rear of the main charge.
Insensitive high explosives may become more common in the next 60 years. A new generation of IHEs has apparently already been tested with the Hellfire missile, among others, and proven to perform just as well as the compositions currently used. Either way, though, you'd have to get a mighty wallop into the main charge to set it off -- I seriously doubt LMG ammunition would manage this, even with older, more sensitive plasticized HMX compositions.
Assuming you get insanely lucky and your LMG round does detonate the main charge, since the projectile deforms the charge prior to and while it's setting it off, and because the detonation originates from another point and in a different manner than what would occur if the fuse detonated it, it would most likely fail to form a projectile from the charge liner. Which makes little difference, of course, since any armor piercing effect would be directed forward and away from the aircraft.
If the missiles are small, like the rocket/missile thingies mentioned in the SR3 core book, the effect on an armored vehicle would thus be minimal. If the missiles are a lot larger, like the naval scale missiles in Rigger 3, there might be trouble. Of course, the larger missiles are even more likely to use insensitive explosives and have even more stuff inbetween before the bullet gets to the explosives.
As Frag-o Delux said, the kind of missiles you'd expect to see mounted on aircraft use solid rocket fuels -- for example, XLDB in the case of the AGM-114 Hellfire. According to some patents relating to such propellants, they may be ignited for example when the metal casing surrounding them is cut. (You can see the layout of the Hellfire motor
here.) That'd mean a pyrotechnically initiated explosive projectile may well have a shot at igniting the fuel, though whether this is something like a 1/10000 or 1/5 chance, I have no idea. If the fuel is ignited in this manner, I expect the rear of the missile would disintegrate and spew out a lot of flames. It would have little effect on surrounding armored surfaces, however.