Yes- you won't have superlight parts, but you should be able to get a very good bike for less than $2k. It won't be 20 pounds, but I think you might hit 25.
I plugged in typical numbers for all the other parts- you may be able to do better, or get lighter parts for about the same price. You could actually go quite a bit cheaper on the wheels, but I put $400 in there to show that even with a pretty good wheelset you can come in under $2k. If you can't get or don't want the Tower Pro fork, you should be able to find another air fork at around $400 - 450.
My build cost me around $2400 (at first
), but I had the frame painted, went with an XT group, a Rockshox SID, and got name-brand carbon parts for the handlebars and seatpost. I put together a spreadsheet to compare the cost and weight of different options- this will really help you decide where it is worthwhile to spend a little more or where to save some $$$.
You'll need some tools as well, but you should already have a lot of what you need if you do any maintenance on your bikes- bottom bracket tool, cassette lockring tool, etc. You don't have to have a repair stand to put the bike together- I did it without one, but then I bought a stand afterward- having one will make it easier.