What if you were a Capitol citizen who was of the age of the District children who could fight in the games, could you as a Capitol citizen be able to participate in the games if you wanted to? Like you were someone who enjoys killing so much that you wanted to actually join in the "fun" and take peoples lives, but were from the Capitol would then you be able to join or not?
I don't think so.
As mentioned elsewhere - here in comments and in answer linked - Games were a form of punishment of rebellious Districts. Participants are drawn from children inhabiting every district. So this right here made any Capitol dweller not eligible.
But I think it was not impossible if one is willing to relocate. There were Districts which were such in name only - i.e. the one where "police" was recruited. No problem whatsoever to make it official. It would be legal fiction, of course, but would work. But looking at the "quality" of the Capitol populace I DON'T see the possibility of anyone to grow there lusting for thrill of the Games... We know it was somewhat that way in "security-related" districts, but... Capitol? Come on...
Like President Snow and Mayor Undersee bot said in their speeches before the 74th and 75th Hunger Games, it was the people in the districts’ faults, not the people in the Capitols’. But Capitol people had more ability to travel than people in the districts, so the Capitol child/teen/preteen MIGHT have been able to go to one of the poorer districts where there are no volunteers and they could volunteer for the person Reaped.