Is it possible to plug in a digital Camera to a computer (nikon d50) and have it act as a webcam?

No. SLR cameras are designed to do one thing and do it very well. Because of the way SLR cameras are made it is not possible to use them as web cams

I am wondering why you would want to use a $1200 (without a lens) to use as a webcam (about $40).

the D50 is an SLR it takes 1 frame at a time on demand.

web cams are low resolution Video cameras which are constantly recording frames and sending them to your Instant Messaging application for further transfer to the internet.

it is a big differance. it would be technically possible to achieve this with the D50 using say Nikon Camera Control pro set to take a pic every .2 seconds in time lapse mode .
you would have to send the frame to a file that only displays 1 frame and deletes the old when the new arrives .

However as pointed out the cost is prohibitive compared to a web cam [ $ 20 to $50]

Good luck

Mike