I'm currently banned on Stack Overflow because multiple people in my office use Stack Overflow, and we share an IP address, so I was suspected of being a sockpuppet. Won't this also happen if someone uses a system in a public cafe?
Multiple people using the same IP generally aren't merged on that basis alone. If those accounts start voting on each other's posts or doing miscellaneous other things that makes it look like they're controlled by the same person, then mods will usually merge them/ban the person for sockpuppetry
This boils down to using a computer responsibly.
From my point of view, however unfortunate: a publicly accessible, web connected computer cannot necessarily be used responsibly.
You are responsible for your account, and what goes on under the guise of your account, and if using a computer with shared access then you are at risk of abuse by others, which inflicts upon said account.
So, to that end, the answer to your question is "no", this won't happen because you're using a public / shared computer (indeed, the system knows nothing of the machine itself, potential access, etc.) and is a consequence of it being misused.