When pump talks to a DHCP server, it overwrites /etc/resolv.conf with the
site-specific resolver information. In many instances, I would like to
use a constant domain search path, regardless of where I am.
Might it be possible for pump to emit a fixed "search" line in
/etc/resolv.conf whenever it rewrites this file?
Already happens. Check man pump and specifically the section on pump.conf.
Basically, just create an /etc/pump.conf with contents of
domainsearch "mydomain.org redhat.com"
and it will always set the search path to what's specified