If you're talking about standard definition stuff upscaling, then yes it'll happen. Videos don't magically gain pixels when we play them on higher resolution screens.
Your SD still will look blocky..at least it does to me. :|
fwiw, HD only really denotes resolution...so...yeah you can just refer to the monitor as being a 22" monitor. we will pretty much all assume the native resolution is 1680×1050.
There are a few <24" monitors with 1920×1080 resolutions, so most people assume 1680×1050. In this case, it doesn't really matter, as both resolutions are well above standard definition material.
As for your second line... more or less, your system won't have a problem playing standard definition videos, you might.
What "standard definition" material will you display on your screens? Also, how are you describing standard definition? Anything below 720p? Depending on what you use your monitors for, it might have a different effect.
In this day and age, I would go with an LCD, regardless. I would only use a CRT for very specific applications.