The PPC in fact started with such, and it's only been in the last few years really that the majority of people have gone with creating utterly new characters for being their starting agents rather than using some version of themself as one of their starting agents.

TOS is rooted in such, as are plenty of older spin-offs.

The instant they join the PPC, their experiences and yours start to diverge. The changes will be small at first, but the longer they stay in the PPC, the more they'll begin to grow into their own character. It can get a bit difficult at times reminding yourself, the further you go along, that they aren't going to be getting the same real-world experiences that you, their author, are getting as you go on with your life and they do their job.

Look at Agent Trojanhorse. She started off as a SI. but she's gotten so much development she and her author are two completely different people. Look at Agent Rina. She's not diverged too much from me, personality-wise, but her insanity is definitely growing and it's only a matter of time before she snaps it's going to play a huge part in her character development. By the time I'm done with her, the only things we'll have in common will be our origins and our fandoms.

Oh, and to answer your question: Yes, there are self-insert agents. ;)

Long answer, people sometimes play a caricature of themselves meant to be entertaining. I know that this might be something I'll try, since my flaws would be hilarious when exaggerated. In fact, this is really more a testament to the PPC's general amount of skill when compared to other fansites, considering how easy it is to make yourself into a sue without even realizing it. It takes an incredible amount of both humility and self-awareness to play an unbiased version of oneself. I encourage you to try it, because it can be quite fun if you do it right.

Some people play completely weird agents, which can be interesting if done well and nightmarish X-man Sues on the hypothetical occasion that they are done poorly. Some people play themselves, which has the same risks. However, there's also the option of creating an agent who isn't you necessarily, but some other everyday human.

Often times the present themselves as caricatures of the writer. But others like the more fantastical approach. I think the general rule is as long as it is a well written character and not a Sue (though I do not think the two are anything but mutually exclusive), you can really do what ever. And of course assuming it fits the tone of the PPC.

But keep in mind that here on the board, we are essentially who we are. There might be some differences, but for the most part the board is essentially a place where you can be who you are. The agents are the characters you create for the stories you write or the RP's you want them to take place in. So I hope that answers your question.