Should I prevent a user from navigating away from a form while it is being processed?

I'm designing a CRM (Web-based. Optimized for desktop use. Clients are using Chrome on Windows) which has a lot of forms in order to edit everything. Currently, when you save a form, the Save button transforms into a loading-gif and is disabled (more clicks won't do anything) and if successful back to the save button with a success message.
It should be mentioned that the user edits detail-information inside the form. So the same form can be edited multiple times consecutively.

Normally, the user doesn't has to wait more than 1 second until the form is processed and saved. But what if it takes longer?
Currently the user is able to navigate away before the form is saved, if the processing takes a long time. The saving-process is asynchronous, so it still will be saved. But if an error occurs, and the user is on a whole different page, the error message won't be displayed.

So should I stop the user from navigating away while the form is still processed?
If yes, how? Overlay over the navigation? Over the whole screen? Info-Message that if navigating away, he won't be notified if there is an error?
If I shouldn't stop the user, how should I inform him, if the save-process was successfull or failed?