Some ships/lines do have internet (probably very bandwidth-limited). The ship I sailed on certainly did (all crew members had at least e-mail accounts and there were wifi points onboard) but whether the crew will let you sign up is something else. Some lines/ships/crews will assign you a temporary shipboard e-mail account (as data usage is probably low if no attachments added).

But you're right that if you want to guarantee access, you do need to bring your own device.

It would appear that some Hanjin ships (the ones that take passengers are generally German-officered so the ships may have German owners) allow passengers access. The link I posted about an artist stranded aboard the Hanjin Geneva (German flagged FWIW) off Japanese waters must have as she's posted photos.