Computer can't resolve other computer names
Windows domain member computers will, by default, automatically add the domain's name as a DNS search suffix. For non-domain member machines (or non-Windows machines), though, providing the domain name via DHCP or specifying it in a configuration file are typically the only means used to configure a DNS suffix.
If I were in your position I'd figure out what "breaks" on "some linux servers" (sic) and resolve that problem, as opposed to trying to cook up some non-standard way to provide the domain name to client machines.