First off, yes, UA does comp, however only to Premier Executive. It is very very rare to be comped to 1K, Unites Highest Level.

Second, there is an enrolment gift, however I'm not sure if it applies to those comped, and even if its still in efect...

As a new member, for your first Economy flight in Y ot B class...5,000 bonus miles

As a new member, for your first Business flight in C or D class...10,000 bonus miles

As a new member, for your first First (class) flight in F, A, or P...15,000 bonus miles.

As a new member, your first booking on UAL.com get you...4,000 bonus miles

Hope this helps!

ZACH