Will using hreflang tags (sitemap links) for Australia, Canada, UK, etc. provide better rankings on other international English Google sites?

Hi,
The language annotations are a best practices conducive to a better organization of your web pages within country and language SERPs. They won't provide higher rankings.

They will, however, produce a better experience for users who will find content that is intended for certain geographies, so if by "better" this is what you were asking, then it could be. Typically, if you succeed with your SEO program in country-specific campaigns, chances are that the localized versions of the content will also rank in the local version of Google.

The example above is correct.

The tags are intended to guide the crawler to achieve the "best fitting" content for the respective region.

These will "not" increase your SERP position. Though these are best-practice mechanics, that definitely increase your user's experience coming from SEs.

Additionally, you then have better control over the content you "know" will be served to the right user coming from search engines. Hence you can display custom content respective to the user's origin.

Pretty cool, right. Regarding you could serve different lead-magnets with knowing the right audience will see them.

First, you need to stop thinking about SEO as a "bag of tricks" to rank more highly in Google. "Will this get my website to rank more highly?" is the wrong question to ask in 2016.

The better questions to ask:

"What does my target audience want on a website, and how can I be the best one to give them that in the best way?"

"How can my website delight my target audience?"

Google is increasingly rewarding websites that provide a good user experience. If Google ranks websites highly that annoy people or return bad information, then that makes Google look bad in the minds of searchers.

In that context, hreflang tags are meant to provide a visitor with the optimal version of the site that it tailored to his or her country and language. So, in a way, it may help rankings in those locations if people have better, individualized user experiences. But you've got to start by looking at this issue in the right context.