Nope. HD CRTs suffer from no input lag.
Scaling? CRTs don't have a fixed resolution...
As a gamer who has played Battletoads on NES (A platformer that requires split second timing) I have not noticed any input lag or blurring compared to how I played it on a LCD.
The game looks better in 480p. Or shall I say 540p mode.
It's impossible to have an informed discussion on input lag based solely on what people notice. Different people have different tolerances for delay (even enthusiasts won't notice it, at times). It's a legitimately hard thing to measure, as people generally don't go out of their way to set up a high framerate camera comparison. And you definitely can't assume that Battletoads is demanding enough that a couple frames of lag would significantly harm your performance in it.
But, as said by me and now dark10x, despite CRTs not having fixed resolutions, HD CRTs do scale images. What happens when you bring up your TV's OSD while running a low resolution source, after all? Are you honestly telling me that your 2000's HDTV has a scanline-laden 240p configuration menu?