Tracking a lost iPad using Find My App without losing personal data

I have two iPads. One for work. One for my personal life. Each has its own unique Apple ID. Yesterday I left my work iPad in the backseat of a taxi. I want to track it using find my app, but I have no other device logged into that Apple ID. Can I log out of the Apple ID on my personal iPad, then log into my work Apple ID and accomplish using find my app to track my lost iPad? If I can, when I am done tracking the work, Ipad, can I log out from my personal Ipad and log back into it with my personal apple ID without every losing any data on my personal IPad..?

[Re-Titled by Moderator]

Original Title: can I log out of my ipad (icloud), log in to another apple id, then log back into my original apple id without losing any data?