After the last few years, I'm surprised they can get anyone to ride the Giro. Maybe the Spaniards (apart from Kelme) were on to something.
But seriously, I'm guessing "no," because I doubt they don't have sufficient sponsorship dinero for two grand tours, and the squad just isn't deep enough. Many of the same riders would have to do both tours, which would put their performance in the TdF at risk. The TdF gives the most sponsorship bang, so I don't think they'd want to risk blowing that. Especially given the scandal potential (sponsors hate that!) that the Giro seems to regularly offer.
It might happen someday, tho'. Maybe after Lance gets his 6th TdF?