"If I register Democrat, can I still vote Republican?"
Absolutely! Remember: Democrats elected Reagan (two terms by landslides) Bush (one term by landslide, lost to Clinton by a squeaker) Clinton made a disgusting spectacle of himself proving that Democrats are disloyal, Bush came back with a rally -- twice, thanks to the Democrats, and I don't see that Democrats will support a wimp like Obama.
They have better sense than to support a loser like Obama bin Laden.