No. Sub-tasks belong to issues, and it's the issues that go into sprints.
It's really not a natural behaviour in "business projects". If you're implementing some form of Agile planning, then the sub-tasks need to remain with their parents, and that's how you plan. If you find this doesn't work, your "business project" is paying lip-service to being Agile and really doesn't get how the planning works at all - they should move to Kanban, or skip Agile completely.
Kanban doesn't allow planning because it's aimed at processes that don't need planning. Scrum does planning on a "commit to deliver X amount of stuff in timeframe Y" I suspect your business projects are quite simply not Agile, and you're trying to apply an inappropriate methodology to them. You'll need to analyse what you *really* want from planning (and maybe just add in the use of Kanban boards for nothing more than a bit of visualisation and easy updates)
I have multiple projects that use variations of the same base workflow. The variations depend on the requirements of the project or issue type. The variations mostly come in the form of new statuses ...
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