Actually, if you're not married when your hypothetical child is born, he/she
WON'T be considered a UK citizen - they will only get the US citizenship from you. Once you marry the child's father, then the citizenship will be conferred. But until that time, the child won't have any more
right to live in the UK than you would.
And you can't take for granted that you'll get approval for mutliple "visitor visa" applications. What happens if you get turned down because they think you're attempting to "settle" without going the appropriate route? And those visas cost money, as do the trips back and forth.
I'm curious about this "sponsorship" visa your friend has, as well. Because there really isn't any such thing. You either come over as a Fiancee, a Spouse, an Unmarried Partner, on a Work Permit or as a Student. If you have a direct parental claim to UK citizenship, that is an option, as is the Highly Skilled Migrant Program. But as far as I know, it's really not possible for a person to simply "sponsor" another person to live in the UK...
Also - if you are in the UK as a visitor, you cannot work or even seek work - or even volunteer to pass the time.
I'm not trying to come down on you - but there is a lot more to this than simply upping sticks and "moving" without any sort of true settlement visa.
EVEN with prior visa clearance from a British Consulate in the US, an Immigration Officer at the UK port of entry would be able to deny you entry if he/she feels you obtained the visa through any sort of mis-representation. And coming in as a "visitor" when you intend to "move" to the UK could be construed as mis-representing your situation.
I always like to see anyone's immigration to the UK run as smoothly as possible - because, you see, mine didn't.