I don't know what you red about Russell, but in my own readings he has always been presented as a fervent atheist, so except with a far stretched interpretation of "neutral monism" as some form of gnoseologic divinity, it's hard to imagine such a character looking for any god.

Also Russel himself ruined the cathedral of Frege with its eponymous paradox, he was clearly among the best to understand how a thing like Godel's incompleteness theorem could come along the way.

And for his relation to madness, his personal life have been felt with many turmoil from an early age. If anything it seems that mathematics saved him, preventing his early desire for suicide.

https://plato.stanford.edu/entries/neutral-monism/

https://en.wikipedia.org/wiki/Copleston%E2%80%93Russell_deba...