No, Charles Manson didn't try out to be part of The Monkees.. This is just a rumour that was actually started by Monkees band member Davy Jones.
There is a Huffington Post article about it that I read and enjoyed.
We know the rumor can't be true because the auditions in question took place in 1965, and Manson was in prison for stealing cars then - and wasn't released again until 1967.
Charles Manson did have some contacts in the music business though, and he aspired to be a famous pop star.
The Beach Boys even recorded a song he wrote. It's called 'Never Learn Not to Love'