This is essentially the exact setup I have. I have two 19" LCD's one connected to the DVI output on the card and the other connected to the analog outpt...and it works perfectly. I am a little picky, so I spent hours messing with the color and contrast settings trying to get them to match perfectly...in the end it is not possible to get a digital and analog signal's color rendition to look the same. After about a week I adjusted to the difference...I could have saved a lot of time if I had simply let my brain do the adjusting....so there is a tip for you!

edit:
(you can't run an LCD out of a VGA port)
You can if your LCD has dual input. I have Sceptre Komodo LCDs that accept DVI and VGA input