I have a recording program on my computer along with an adapter to plug my guitar into my comp and record direct. (Not good enough/not ready/dont have the money for microphones) So the guitar part is done.

If I am filming along with the playing, can I just sing out loud and have the camera pick it up, if I don't have a good microphone to sing into?

I have a very nice HD camera.. so I don't know.

Basically the question is - Will it work playing direct guitar and take video of it with an HD camera and have the camera record my singing?
the camera mic may do however even high end cameras come with cheap mics these days which is why audio is normaly recorded onto a digital recorder, fixed in ProTools, then synced with the video in Avid. TV Companies and the movie industry almost always use a shotgun mic which range from $100 to over $1,000

for home recordings you dont need much...the on board mic may work well enough but its up to you if you want to get mics and an interface..
Try the on board mic for yourself..