Conserving PageRank by not linking to other sites is a bad idea. PageRank control and sculpting was a good SEO technique 10 years ago, but today it doesn't have the same impact it once did. Even back then, withholding external links wouldn't have increased your sites rankings.
1997 PageRank patent
On the face of it, withholding links from other sites seems like it could give your site a PageRank boost. Google's original PageRank patent indicated that it worked exactly like you describe in the question. Removing the one external link would pass the its link juice instead to the other internal links on the page.
However, Google doesn't use PageRank exactly like they describe in their original patent anymore. They have made many tweaks to it over the years. I believe they have made changes to limit the impact of external links on your own site.
Google also has hundreds of other ranking signals. Minor changes in PageRank (such as those caused by removing external links) would be dwarfed by other ranking signals these days.
Google may even judge a site by the number and quality of external links on the site as a whole. Removing external links may be counter-productive because Google may view sites more authoritative when they link to good resources on external sites.
Back in the PR sculpting days, I did a number of experiments to try to find out more about PageRank and how it influenced rankings. We had a site where the external external links went through a redirect so that we could count clicks on them. Because robots would mess up the counting, we blocked the redirector in robots.txt. The redirect links were very opaque, so bots couldn't even guess the final URL without being able to crawl the redirects. The links just used a database id for each external link of the form
/redirect?link=838838. We realized that this meant that Googlebot couldn't follow the external links on our pages. We wondered if this was conserving PageRank and giving us higher rankings, or whether having no external links was hurting us.
Our site was divided up into a thousands of content areas where internal links on those pages was mostly to other pages in the same content area. We randomly chose half of our content areas as an experiment group and left the other half as a control group. On the experiment group we changed the external links to link directly to the external site rather than link through the redirect script. To judge the effect we measured our SEO traffic to the two experiment groups. We also checked the rankings for some keywords where we had paged from each group ranking. In addition, we checked the rankings for some keywords of the external pages to which we were now linking.
After running the experiment for several months we found:
- There was no change in our own rankings. Adding external links didn't seem to dilute the PageRank of the content groups with external links, nor did it seem to give those groups any sort of SEO boost based on newfound authority. Either the two effects cancelled each other out, or external links just didn't influence rankings.
- The pages we linked to did get a modest increase in rankings based on the keywords we were monitoring for them.
I was a bit disappointed to find that Google wasn't rewarding external links. Given how much Google's algorithm depends on links as recommendations as good sites, I would have thought it would be in Google's best interest to reward sites are good netizens and curate crawlable links that would feed Google's algorithm. However, I was relieved to see that withholding external links wasn't rewarded.
I haven't repeated this experiment in the years since. I doubt the results would be any different today than they were almost a decade ago. But clearly the original PageRank algorithm wasn't used without modifications by Google even then.