Yes, this can happen. One of the user complained that despite SQL Server Express 2012 has limitation of 1GB RAM, its consuming even more.
I noticed that in my server when the SQL Server express 2012 starts, it works with the minimal memory but as the time progresses, it starts consuming more and more memory (I also noticed that the performance of the database decreases). To overcome the problem we need to set the limitation on the memory consumption by the SQL Server 2012 Express. To do that follow below steps
1. Opne SQL Server Management Studio.
2. Right click the server and select Properties.
3. Click on Memory from left panel on the dialogue box.
4. Change the value of Maximum server memory (in MB) to something like 600, 800 or whatever you can afford to spend for SQL Server based on the amount of RAM have in your server
5. Click OK
and you are done. Now check your application that is using this database and you will notice slight improvement (at least I noticed). I also noticed that other application running on the server also starts performing well.