I've tried recording Diablo 2 at 30 FPS using Fraps, but all I get is an audio track with no video. Diablo 1 required a mod to record it, so I'm wondering if Diablo 2 requires the same thing or needs it to be in windowed mode.
The problem is probably due to the rendering library you're using. I say this not because I have used FRAPS extensively, but rather because I know a lot about Diablo 2. Diablo 2 can render in DirectDraw (for use without any graphics acceleration) and Direct3D. However, it was designed to run best with the Glide library, which was designed for the now-defunct Voodoo line of graphics acceleration cards.
The first thing I would suggest is to configure your video settings to make sure you are not rendering with DirectDraw, and try Direct3D. From general experience, I wouldn't be surprised at all if FRAPS did not record output rendered in DirectDraw. If that still causes issues, then I would download the nGlide wrapper library which allows modern video cards to interface with Glide. It also has Blizzard's official seal of approval for use with D2. If you want D2 to run the best and look the nicest, I recommend this option. It is completely free and it's not hard to install either.
In any case, we would need more information to help you further.
P.S.: As a literal answer to your explicit question, yes, it is definitely possible, since there are many YouTube videos of Diablo 2 footage. If all else fails, you can try OBS, which I believe allows you to stream to a file (also known as recording, heh) instead of a livestreaming website. OBS allows you to capture your game application's output, like FRAPS does, but it also gives you the option to record everything being output on your screen. The latter option is probably a surefire way to get your game recorded if all else fails.