Absolutely. But then serverless is not necessarily a good solution. The point is that if you have that as a requirement you would likely pick a portable solution such as containers.
The data question still stands. It’s possible but limits your possible solutions.
Those are business constraints to which the current serverless solutions are a poor choice simply because you’re unlikely to have the support ecosystem to rely upon (yet).
Aka we don’t have the tools for it.
But I would still argue that those situations are highly unlikely except in public sector or similar.