While I don't really feel comfortable answering this on behalf of the "incredibly funny" people, I can at least give you an answer of what how working to become a comedian impacts your relationships and social interactions.
There are certainly some advantages. It's a lot easier to make jokes in conversation once you know how to interact with a crowd and craft jokes on stage, you get to meet and work with some famous people that you would otherwise have no business knowing, and there is no feeling in the world quite like having a great set and then have people come up to you after the show and tell you how much they liked it. But when it comes to dealing with your personal relationships, it can be more of a hindrance than anything else.
One of the biggest challenges for is that the best way to come up with material is just to constantly be thinking about what's funny about our every day lives. So for me I often times spend too much time people watching or over-analyzing every situation I'm in rather than just being in the moment and enjoying it for what it is. If I'm at a baseball game, I'm focused on stupid people in the crowd, or if I'm out to lunch with friends I'm thinking about material about people complaining about their food.
I try to compartmentalize my life so that there are times where I just don't think about material (like when I'm at work or at some sort of family function) but as soon as I start to get bored my mind usually drifts to trying to find the absurdity in the situation that I could make a joke out of.
The other thing that's hard is that it's a job that most people don't really understand, but are totally fascinated with and usually have some sort of concept of what they think "being a comedian" means. So as soon as someone at work or at a party finds out I'm a comedian, I usually end up having to spend a few minutes explaining to them that I have to spend four or five nights a week out at open mics or shows working on material and that crafting a joke is a long process. It's not like I can just go up on stage and start talking about my day and be funny every time.
For that reason I don't hide the fact that I'm working to become a comedian from anyone, but I don't advertise it either.
One of the other issues is that there is always a sense of insecurity that comes with being a comedian and that always bleeds into your everyday life. Comedians tend to be outsiders of some sort. It could be something like having anxiety, or some kind of weight problem, or your sexuality, or something about your beliefs not lining up with your family's beliefs or the cultural norms you grew up with. And on top of that, now we are doing something that is further outside the cultural mainstream by spending most nights out at bars and clubs rather than focusing on getting a promotion at work or spending time with a girl to finally settle down and get married.
Whenever you go home for the holidays, you start to learn that your story of what you've been doing is vastly different than everyone else's story about going to grad school or working their way up at their company. And even if everyone is incredibly supportive, it's hard not to feel different than everyone else. Despite the fact that that is exactly what we're shooting for, it's a bit unsettling nonetheless.
On the other hand, at this point about 90% of my friends that I see with any regularity are comedians, so we are able to bond over these things just like any group of people who work in the same field. We have our own social rules in some ways where we will purposefully take jokes too far, and we say the C word way more than we would around non-comedians (That may just be a Philly thing, but it does get said a lot to describe anything from another comedian, to a bachelorette party in the crowd, to a pen that won't work).
Plus, being freinds with comedians makes my facebook feed worth reading. Rather than seeing pictures of what someone at work ate for lunch, I just get to hear some of the funniest people in the area joke about whatever is going on.
So in effect, there isn't that much difference between comedy and any job that requires a lot of time and effort. I'm sure during law school that law students hang out with a lot of law students, and that after they graduate they hang out with the lawyers they work with. Just throw in some more anxiety and drinking and you have the life of a comedian.