My site is being hit multiple times per day with referral traffic with 100% bounce rate and 0 seconds spent on site. Can this negatively affect my google page rank?
Yes Ofcourse, Its a red sign for you Check if your site traffic comes from a a specific location then block it, and stay safe from a big panelty.
Google PR is irrelevant nowadays. But if you are talking about your SEO efforts then yes it will have some impact. If you think you are getting spam traffic then manually block it on your analytics. It is also to avoid unnecessary data on your analytics traffic.
Spam traffic is really a big concern to you. You must have to block it through .Htaccess or by robots.txt.
Off course that will effect negatively in Google page rank. You have to find out how to prevent this trends.