Yes... and no. There's no simple way to do it for the most part, at least not inherently. Read, for example:
to detect the effects of the popular
Adblock filters. This has been
done by generating a honeypot-like URL
and verifying its delivery and also by
more advanced verification of the DOM
after the web page is rendered in the
web browser to ensure the expected
advertising elements are present.
These methods do not detect the
presence of the Adblock extension
directly, only the effects of the
filters, and are vulnerable to
continued updates to the filters, and
by whitelist-filtering web scripts
with an extension such as NoScript.
An attempt was made to detect the
plug-in itself but that detection
method was rendered unusable by the
0.7.5.2 update of Adblock Plus.
So it's more trickery and picking up that the extension is present by finding the side effects and making an educated guess - but they can do it for some things.
As for hiding this information from a server, I don't know - it is probably possible but I know of no method.