PVMs (and similar CRTs) are about equal in image quality and lag. Perhaps even better, because they are usually made for exactly Melee’s resolution (480p60), while PC CRT monitors are usually geared towards 1200p85.
This results in PC CRTs having more of a scan-line / sharp look, while PVMs look more “uniform”.
I have both and kind of prefer the PC CRTs, because they are quieter, but really both are perfectly fine and much better than the abundant 480i60 TVs.
That device is not the state-of-the-art for component→VGA conversion. I wrote a review on the Extron CVC 200 on page 3 or something here, and I really recommend that one, especially considering it’s often on Ebay for ~20$ in the USA.
But, yes, using Wii component cables and an Extron CVC 200 (+ a 5-BNC to 5-BNC or 5-BNC to VGA cable) will allow you to connect to any PC CRT and play on that just fine.
The BNC inputs on PC CRTs expect standard RGBHV video. Most of them accept RGsB too. But there is no way to get the Wii to output one of these through the component cables (with 3-RCA connectors); that one will always output YPbPr. (Sync is sent on Y channel.)
You do get a picture by connecting the Wii component cable, but there will be green tint. I was not able to find example pics on the internet, so I hooked up my Wii to my Mitsubishi 2070SB directly and made photographs. The green tint is a bit less pronounced than in real life due to automatic white balance that seems like it can’t be disabled entirely.
Why is that, you may ask?
To put it short, if we have a gray color, in RGB it would be about:
G 0.5
B 0.5
R 0.5
While in YPbPr, it would be:
Y 0.5 (total brightness)
Pb 0 (positives denote blue shift, negatives denote yellow shift)
Pr 0 (positives denote red shift, negatives denote green shift)
Now what happens is that the Wii component line that carries sync is the Y one, so by connecting that to the CRT green line, it will read a higher offset for that color than for the other dimensions. The CRT assumes the YPbPr values to be GBR values, so all near-grayscale colors are interpreted as green.
If you are okay with that much green tint, sure, just buy the adapters and make the connections. But I think the 20-30$ for an Extron CVC 200 to get proper colors are easily worth it.
Here’s a picture of a high-res CRT PC monitor with 480p Melee (from Gamecube here, but Wii+CVC200 looks ~95% identical) where you can see the scanlines when viewed in full-res:
Here is a Sony PVM, for comparison:
(For this one, I cranked up brightness and contrast all the way so that with lowest camera ISO setting the picture is still distinct enough; in real-life, the colors on the CRT PC monitor are almost identical when viewed side-by-side. Also, I took these pictures on different days and times, so the lightning was different, causing some change in color white balance too.)