Yes, you are exactly right. Public school prayers were banned by the Supreme Court beginning in 1962 with 'Engel v. Vitale'.
Despite rumors to the contrary, that decision does not quote Jefferson's Danbury Baptist letter. It does quote James Madison:
It is proper to take alarm at the first experiment on our liberties... Who does not see that the same authority which can establish Christianity, in exclusion of all other Religions, may establish with the same ease any particular sect of Christians, in exclusion of all other Sects? That the same authority which can force a citizen to contribute three pence only of his property for the support of any one establishment may force him to conform to any other establishment in all cases whatsoever?
Engel v. Vitale