Yes, it's possible, but not practical.
It's not practical with a computer DVD writer because you would have to install a capture card or tuner in the computer, then have the appropriate software to record the captured video to the computer's hard drive. Then you would be able to view the video on the computer. If you expect to play the video on a DVD player there is a lengthy file conversion process before the video is burned to a DVD that may be played in a DVD player.
It's easier to connect a DVR's S-Video or composite video (yellow) output, plus the white/red audio outputs, to the corresponding input on a stand-alone DVD Recorder and record to DVD from that input while the video is being received or played by the DVR. After the DVD is recorded and finalized it may be played on regular DVD players. New entry-level stand-alone DVD Recorders are priced around $100.
Stand-alone HDD/DVD Recorders are more versatile than direct to DVD Recorders in that material may be recorded to the internal hard drive through the S-Video or composite video (yellow) input plus the white/red audio inputs, edited/divided and then high-speed dubbed to DVDs. After the DVD is finalized it may be played on regular DVD players. A like-new refurbished Magnavox 2160 HDD/DVD Recorder is currently priced less than $160 at J&R World:
(I own four of these outstanding Magnavox 2160 HDD/DVD Recorders, one purchased new from walmart.com and three purchased refurbished from J&R World.)
At the AVS Forum the first post in Wajo's sticky thread is the gateway to a wealth of information concerning Magnavox HDD/DVD Recorders: