One could argue that Cushing --> obesity + insulin resistance --> GnRH dysregulation --> PCOS (since PCOS is known to stem from this).
But in a more broad sense, multi-organ endocrine hyper-/hyposecretion is characteristic of polyglandular syndromes. Individuals with endogenous endocrine dysregulation are at increased risk of dysregulation elsewhere. For instance, if a patient has ANY autoimmune issues (e.g., DM-I, RA, Graves, etc.), you always screen for other common autoimmune issues.
That being said, if I diagnosed Addison in any pt (e.g., high ACTH/low cortisol; high renin/low aldosterone), I'd probe thyroid and glycaemic regulation. Patients with Addison would be at increased risk of Graves or Hashimoto. Hashimoto --> high TRH --> high prolactin --> GnRH dysregulation --> anovulation. And of course dysglycaemia can cause PCOS on its own. Those are just broad pathways for discussion.