tl;dr: Adjuvants may increase the response of the immune system if given without an antigen, but that immune response would not be directed towards the existing pathogen.

The reason behind this is tied to how the immune system targets a pathogen in the first place. The initial step is chopping up the pathogen/virus and creating antigens by the first line responders (known as antigen presenting cells, or APCs). These cells then give two signals to other white blood cells to induce the immune response: the antigen and the biochemical signals (cytokines) to teach the WBCs how to break down the pathogen. Without both signals, the antigen AND the cytokines, there is no further immune response.

Some adjuvants (aluminum/M59) increase antigen processing while other adjuvants artificially provide instructions on how to combat the pathogen. Without an antigen associated with the adjuvant, the immune system would fail to create any immune response to target the pathogen even if it's already in the body. Failure in this two-signal process is mirrored in some inherited auto-immune deficiencies as well as immune evasion of cancer cells.

If you're interested in a relatively recent update on how adjuvants work, this literature review go over recent advancements.