No. DVDs use smaller data pits than a CD does, so DVDs require a laser capible of a smaller bandwidth. A DVD player can read data off a DVD and can also read CDs; however a CD player is not able to read the data off a DVD. If you don't have a DVD-Rom drive, then your computer won't be able to read DVDs. You might as well stick a coaster in the drive, because a CD-ROM drive won't be able to get the data from the disc.
You can read more about DVD vs CD here:
http://www.crutchfieldadvisor.com/learningcenter/home/dvd_closerlook.html
Now, if you had a way to hook a standard DVD player to your computer to record the video imput (the same as hooking a VCR, TV, or video camera to record video), you still might have problems getting the video to appear on your screen, as many DVD players have internal devices to prevent boot-legging or copying, so it scrambles the export singnal when going into a VCR, computer, or other recording device.
Long story short, with out a DVD-rom drive, getting screen captures from a DVD is quite a task. And it usally ends up being easier and cheaper to just to get a DVD drive.