There should be no problem whatsoever running SP in a sub-domain install of WordPress.
Simple:Press does require the page (defaults to ‘forum’) for it;s display but you can set the page to be the front page of your website. See this FAQ for more info: https://simple-press.com/documentation/codex/faq/how-to/how-to-make-your-forum-display-on-the-front-page/

I understand this, my question is about loading the forum (only) from the sub-domain, assuming that your WordPress installation is on the root domain  

It’s my understanding that unless WordPress is installed on the sub domain you won’t be able to run Simple:Press. Although I’m sure Andy or Steve will correct me if I’m wrong there!

That;s right. It’s a WP plugin. It needs WP installed to work.