The body's mechanism for detecting foreign object has a built-in failsafe that minimizes the likelihood of misinterpreting a self-derived antigen as foreign.
Immunologic tolerance (unresponsiveness) normally prevents reactions
against self-antigens; if immunologic tolerance is broken, autoimmune
reactions may occur. Much of the development of tolerance occurs in
the thymus by the elimination (clonal deletion) or inactivation
(clonal anergy) of self-reactive clones of T cells. Other mechanisms
of tolerance occur extrathymically and include activation of
antigen-specific T suppressor cells and clonal deletion, which results
in the elimination of self-reactive B cells or T cells, and clonal
Basically, before a T cell starts looking for potential antigens, it generally first spends some time in the thymus being tested against antigens which are native to the body. If it responds to such an antigen, the T cell will either be destroyed or deactivated.
Having unnatural amino acids as part of this process is unlikely to change its efficacy. T cells which would target peptides with these unnatural amino acids will still be checked against the body's cells before being sent out to do their work; the mechanism would work the same way. I suspect that the rate of autoimmune diseases would be unchanged compared to normal organisms.