If the processing job is of a larger scale, perhaps a notification center / job queue listing could be a better combination?
You can give the user a continuous feedback on the processing via web socket messages, there are so many ways to accomplish this kind of functionality, it all depends on what you would like to give back.
If the user is logged in with a session/token you can subscribe the user to a unique room where you send messages directly to this user, on progress or final completion.
What do you mean by safe? Risks? Important for client to get a feedback of the processing? Client may leave the site and come back later, doesn't retrieve the message because it's event based, unless you store the feedback in a queue that is delivered when the user is online and you only remove the message from queue once the client replies with a 'notification-read' message.