I find no record of cavalry storming through breaches; I'm not going claim this didn't happen as I don't have many sources on the subject one way or the other - but I doubt it ever happened; its certainly not what I would call plausible. The notion is silly, and especially in light of the knowledge that all Knightly warriors were as comfortable on foot as they were on horseback, there would be no militarily sound argument to ever waste their mounts and risk their lives in such a manner.

Lighter cavalry would man pickets - as you said; but there are other roles they, and heavier forces would play during a siege. Food, water, information - all are nominally cut off when a siege begins (be it in the modern sense such as at Leningrad, or in a medieval sense). However, trickles could still come through, Cavalry pickets were for more than just preventing a sally, it was to make sure the siege remained as air-tight as possible, warned of relief attempts, and interdicted supplies. For defenders, Cavalry would often lead sallies, and raids: Food and supply is as important to the besiegers as the besieged. Foraging parties, isolated patrols, etc. - all are tempting targets for active patrols and an excellent way to 'bleed' the besiegers. It also provided opportunities to destroy or disrupt actual elements of the siege; again I'm going off more modern knowledge but a common goal for a sally would be to spike cannons and disrupt the making of siege trenches; I'm sure disruption of an enemy siege camp, and the physical destruction of siege equipment was at the forefront of potential objectives for a sallying defender.

The battle of the Herrings, for example: This battle began as a (predominantly) French raid on an English supply convoy carrying food and ammunition to the siege camps. The assault was repelled by using the supply wagons to form a laager. Had the battle gone to the French, they would've had the triple windfall of securing great stocks of ammo, great stocks of victuals and of destroying a significant portion of the enemy force. Actions such as this, miniature though they may be, have long-reaching effects on a siege.