Like I said...you need to read the Constitution.
Lemme help: Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances
Did you get that?? 1 person, regardless of their employment status, who prays, is in NO WAY ESTABLISHING ANY RELIGION. He is merely exercising his 1st amendment right TO PRAY, that the GOVERNMENT SHALL NOT PROHIBIT
So NO, the Constitution is NOT against a public employee praying.....especially if its open to the public. That's the foundation of freedom, and not illegal, in any way, shape, or form