No, that is not what it is designed for. Tempo (Timesheets) is a time tracking app where you log work against Jira issues. Theoretically you could attach your documentation to the issues you are logging absence against.
However, I would strongly recommend you not to do that. Medical records are private data and you don't / won't share that publicly, right? The usual way to submit this type of information would be in or through a dedicated HR system in any organisation I've ever worked with.
I can imagine you are thinking about reducing the number of administrative steps you need to take when reporting illness. You might have a look at integrating your HR system with your time tracking solution so that illness, training and holidays e.g. are registered in the appropriate system, but synced to your time tracking. That may be a more robust solution.
Hope this helps you in the right direction!
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