Only you can know after you've tried it.
Will linking to one of your blog posts from your homepage increase its keyword rankings?
I, or anyone else, cannot say.
It will increase the PageRank of Your Sub-Page tho
Linking to any sub-page from your homepage will result in a net-gain in PageRank for the sub-page.
This is because of how PageRank flows throughout a website.
Diagram is for conceptual understanding only. The actual amount of PageRank that a page passes to its links is unknown.
Keep in mind, PageRank is just one of many rankings factors. It is not special like it used to be. So it's totally normal for a site with low PR to have high rankings.
Broadly, you should look to increase your E-A-T (Expertise, Authoritativeness, Trust) while maintaining a regular publishing schedule, and also building a link every once and a while.
That does the trick for most sites.