I don't think there's a correlation between writing a blog and being a good developer.

I think there's a small correlation between "having a tiny bit of evidence online that you're capable of solving problems" and "getting invited to an in-person interview" - at least given my own experience at the companies that I've worked at (and hired for).

That said, I do think there's a strong correlation between being good at written communication and being a great senior / staff-level engineer.