If you can find a 120 at a reasonable price, then yes. There's one on eBay, but it's going for $400 plus shipping. Occasionally, they do come up on eBay in the $200 range, but they tend to go fast.
The advantages of the Hydis screen are a high contrast ratio and wide viewing angles. It's quite a bit better than the screen you have now. The 120 is hard to find, but the 100 and 110, the glossy versions of the screen are pretty widely available on eBay. They're also very good if you don't mind the occasional glare. I had the 110 in my X200.
Most of the Hydis screens sold on eBay are tablet screens. They have the touch surface and digitizer attached to the LCD. The touch surface must be removed for the LCD to fit into the LCD frame. You can probably leave the digitizer. I did on my X200. There's some pretty cheap ones on eBay, like
this that are less than $50, but they have nicks or scratches on them. My guess would be once you removed the touch surface they'll be in good shape underneath, but I can't say for sure. Removing the touch surface involves taking a razor blade, and cutting between the touch surface and the LCD frame, ensuring you don't damage the LCD or break the glass. It's pretty strong glue too.
If that seems a bit above your level, you can buy one with the touch surface and digitizer removed, like
this. Also hit the
support and training site. It has videos showing how to complete each step of the process in case you get stuck. The X201 isn't there, but the very similar X200 is. It's beyond a beginners level, but completely doable in my opinion.