I think you'd be better off using something like powershell to monitor drive space on a different server. Though I suppose if you wanted to, you could have the SQL Backup be step one and the powershell script be step 2 in a SQL Agent job.

I would also recommend any other type of monitoring tool out there that can look at Server monitoring and would send you an alert for something like drive space. I wouldn't necessarily expect to do this as a function of SQL Server.

Just off the top of my head, SpiceWorks or FogLight are good tools to use. I'm sure other people have their favorites to use.