Am I correct in assuming that proper bile function is also good for the immune system and that GALLMET has a positive effect on this?

Bile and bile acids have an antiseptic effect, which comes from their fat breakdown action, as bile acid breaks down the outer, fatty peptide shell of various harmful bacteria, microorganisms and viruses, thus helping the immune system. Any bile deficiency is also an immune deficiency, which increases the body's susceptibility to various infections and other diseases. If bile is not produced in sufficient quantities, this antiseptic function does not work properly and replaceable by taking bile acids orally.
Bile acids also protect against endotoxins (internal toxins). Endotoxins are released from bacteria that have decayed in the gut, which, if absorbed into the circulation, can trigger pathological processes. Under ideal conditions, however, bile acids protect the body against endotoxins present in the gut.
"In the physico-chemical defence based on the detergent effect of bile acids, we have identified a general defence mechanism of the organism that is not limited to bacterial endotoxins, but extends to all "agents" (e.g. some viruses) that have lipoprotein or lipoid structures on their surface..." Source: research by Professor Lóránd Bertók - Hungarian Science, 2008/07 page 844