OSX HomeBrew Security Risks

Would Homebrew +package updates have an additive effect with Apple security updates?

It should improve security if you leverage it to regularly update packages that Apple is either shipping out of date, or not maintaining and patching. Example

Does Homebrew have known security issues in and of itself?

Without a full security review this answer is unknown. Worth digging around reported issues for other security related issues.

... Would installing a package manager and associated updates change the system configuration such that, in the hands of a relatively inexperienced admin, it will ultimately be in a more vulnerable state?

This question leaves a lot to speculation. I believe the homebrew documentation and its community is large enough that this should not be an issue. Deeper dive into considering ways to secure OSX.

The first thing the OSX HomeBrew installer want to do is change owner of /usr/local/bin to your local user. Thus making any random executable a major security threat. I'd say it would be hard to expect any security after installing HomeBrew.