It should work just fine. You will have to run the 2nd display on VGA, but it will work. The only thing you might notice is some sluggish graphics depending on what you are doing, but basic stuff should be fine.
Yes it will work. Will you need a dedicated card? Maybe if you see graphic performance issues, but I would do without it for now. And even if you need a dedicated card, you won't need much more than a sub$50 card. The benefit to that would be you can get a dual DVI card.