Does Van Eck phreaking perform as described, i.e. allow a person to observe what is being displayed on a given computer screen (notably a LCD) from a distance without having any physical connection to the machine being monitored, and without the knowledge of the person being observed?
Yes it does. VGA or keyboard cable has side effect of acting as antenna.
Both eavesdropping and countermeasure techniques are widely knows as TEMPEST (which was codename used by NSA). It's described with details and numerous references here. Example from above source:
It is standard to use TEMPEST protected terminals in military (NATO standard requirement), banks, embassies, government installations etc. The buildings themselves are usually also TEMPEST protected. TEMPEST protection of hardware is basically shielding equipment and cables with metal, which acts as Faraday cage. Which also has another side effect — it gives some protection against EMP attack.
BTW. the question gives away the answer. Van Eck's paper was published and peer reviewed.
This video (2:10 onwards) shows Van Eck phreaking working with a CRT monitor, although it claims that the process works through the cable, not the monitor itself; if that is true, then it would work regardless of the display technology.
It also claims that keyboard data can be captured too. I find that difficult to believe.