Yes it does and already is, and as for the harassment the CoS imposes on its ex-members, that's permittable so long as it's at least borderline legal. The Lemon test is very broad.
Lemon got overruled just earlier this year, so who knows now. The test has implications for both the Free Exercise Clause and the Establishment Clause, one of which the current SCOTUS construes much much more broadly than the other, so it's anyone's guess whether they'd jerry-reg some version of it for the benefit of the CoS or not.