(imported comment written by PeterLoer)
It may not be the official supported path, probably because there aren't any tools or guides to check that everything has gone correctly during the migration, but it is definitely doable.
Basically, as long as you can install the full version and make sure it picks up the database contents, existing user roles, etc. from the express version, and is available at the same location, it will work (and in fact IEM won't even know the difference).
I believe all recent versions of SQL server have an 'inplace edition upgrade' installation path which is what you will want; for instance, here is a URL with some documentation from microsoft on the pathway in SQL Server 2012: http://msdn.microsoft.com/en-us/library/cc707783.aspx.
If you have an environment you can experiment in, maybe you can just take a backup and try it out. If you do the upgrade and everything seems to work and all of your operators are able to connect, you should be good.