If I spend some time setting up the hosted demo option for my company, do I lose all the work when I purchase?

No, the trial/demo for EIOBoard is kept exactly as you used during your trial.

Once a purchase is made, and if we are hosting, the only work that needs to be done will be on the back end by us and will be seamless to you and your users.

If you decided to host locally, we would just provide a permanent licensing key and once you installed that, nothing more would be needed and nothing would change.