can opening a pdf reveal my ip address?

I opened my vpn, connected to a location. Then opened my browser, went to a website, and downloaded a pdf.

I saved pdf to usb drive, and copy/pasted the pdf to my other computer which doesn't have a vpn installed. If I open the pdf from this computer, is it possible for the owner of the pdf to see my real ip? can a pdf make any connections, or it's all local? how can I check where it's connecting to?

Yes. Is possible. You can check on and see what IPs/domains it connects to, if connects.