Yes - Firebase has quite a flexible set of options for server-side updates and it is simple enough to schedule a cronjob to connect to firebase and perform some scheduled update or edits.
The most generic approach is to use the REST API to perform your updates although there are specific libraries to support Node and other platforms.
It is worth being aware of the recent major upgrade to version 3 of Firebase which introduced quite a few significant changes - it can be easy to confuse the older examples floating around with the new API so be aware of the differences as you put together your first proof of concept examples.
I assume that you are looking to run on your own server although another alternative is to use a container hosting environment ( Google Apps etc ).
If you have your own server and are looking to integrate I would suggest starting with:
https://firebase.google.com/docs/server/setup#prerequisites
Then perhaps a quick look at:
https://firebase.googleblog.com/docs/web/quickstart.html
and
https://www.firebase.com/docs/rest/
If you are just getting started I would suggest a first task being to authenticate, retrieve and update a Firebase record.
You can configure server auth keys through the FB console and use these as part of you authentication process.
If you are unfamiliar with JWT then it is worth spending a little time getting up to speed on this and working through the examples at https://www.firebase.com/docs/rest/guide/user-auth.html
Further to your comment:
So the first approach that comes to mind is to run some kind of scheduled job in your Cron which would connect using the REST API, perform some kind of query on the existing data to identify those records that require an update and remove or modify them.
Giving a little more though you could extend this approach without having to run at a recurring period less than the minimal anticipated deletion time you could run the scheduler just to clean up at some longer period but filter your results to the client so that you are not including stale data. This approach is discussed a little at Firebase chat - removing old messages
Getting the right solution to your particular scenario will depend a lot on how well you structure your data which can be counter-intuitive; particularly for users who have come from an RDBMS background.
There may be an inclination to keep the data slim and unpolluted with old irrelevant data however Firebase is quite good at managing large minimally structured data and the overhead of this bloat may not be as bad a thing as you may think.
If the filtering itself isn't sufficient and you don't have a server that you can CRON a cleanup process then you can implement a firebase worker process in Node or similar and have this running on a container service such as Heroku or Google Apps. See Firebase push notifications - node worker for some ideas on how to approach this.
When asked Google advised that they didn't advise on where best to host worker services but they did mention both Google App Engine and Heroku.
Another approach if you don't want to implement and host a watcher/worker process is to simply include some code in the client that checks for and removes stale data periodically.
The firebase Queue is very cool but may be a bit of an overkill for simply expiring stale data.