The TU-DST50 downconverts its output to NTSC. If you can get the S-video or composite video output to a conventional (NTSC) video monitor, you can confirm that the data is being received and recorded to (or played back from) the D-VHS tape.
If you can't use the NTSC output, and you don't have access to a component-to-RGB converter (Extron makes one called the CVC200, and Key Digital also makes one) then you might, as you suggested, be able to connect the Y output of the TU-DST50 to the green input on the monitor. I think it has to be the green input in order to get a stable image since sync information is provided sometimes on green but not (I don't think) on red or blue.
This presupposes that the computer monitor will take RGsB input. Many do.