I couldn't find any mention of it in the FAQ, but I read a small tidbit by another redditor suggesting such things probably happened, though the frequency is unknown. I suspect that unless a guard was posted, this sort of thing would happen, especially if the victim/criminal was left in the stocks unattended for an extended period of time.
The only source I could find was http://www.nospank.net/rape3.htm, although without further research I don't know how accurate it is.
It seems unlikely. This essay about sodomy and the pillory (Thanks to /u/CDfm who posted it elsewhere today!) gives pretty much the exact opposite impression actually. Sodomy in 1700s Britain was an offense punishable by death. A convicted sodomite could expect to be hanged. Someone convicted of attempted sodomy would be places in the pillory, and subjected to all kinds of assaults - many apparently died from projectiles that were thrown at them. There is no mention of any sort of raping of those in the stocks though, and given that the act of doing so would itself be punishable by death, it certainly wasn't something that authorities in any way were encouraging or expecting be done to the victim.
The question is a little problematic though, since if it wasn't a 'thing', but rather a creation of more modern minds creating stories, there simply isn't going to be much literature that focuses on saying it didn't happen. Instead, base don a few searches I have done, the best proof of it not happening is more the lack of sources speaking to it, especially ones like this where it would seem to be a rather important fact to mention, if only in passing.
Now, the only caveat I would offer is that this only speaks of men placed in the stocks. Whether women who were subjected to the pillory were the victims of sexual assaults while there is not addressed in the paper I cited, but that might be a possibility.
Okay, so, other folks have contributed here perfectly cromulent answers, but let me expand upon it a little bit.
Were folks at the stocks/pillory raped?
No. We can't be 100% sure, but we can be six sigma sure. Here's why I say this:
The stocks were a place for social approbation. It's a form of social control. By putting people in the stocks the authorities are displaying the transgressive individual for all to punish. So, the entire community shares in the punishment by beatings, throwing waste, etc. By sharing in the punishment the community is reinforcing social norms. Had someone been sentenced to the stocks and the community didn't agree with the punishment they could have easily been sprung the prisoner. So people who are sentenced to the stocks are consensus criminals.
Okay, now, that's great, but what does it matter? It matters because you don't punish a transgressive criminal by doing more transgressive things. Rape is one of those crimes in early modern England around which there was consistent agreement. Rape was notoriously difficult to prove, of course, but the foulness of rape crossed social boundaries.
Now, you may be wondering, if murder is also transgressive then how is execution permissible? It's permissible because 1. it's supposed to be built on social consensus and 2. the criminal, by committing murder, has put him or herself outside of God's law. And this brings me to my final point: rape also puts someone outside of God's law, but it cannot be punished by rape because that is an individual act, not a community act.