Yes, you can use it even after expiration of MATLAB.
MATLAB compiler builds standalone application (exe file) from the code written in MATLAB. Once you are all set with the customizations, while using MATLAB Compiler for your application, you have the option to package in the Automatic Installer for MATLAB runtime libraries. The application will use these runtime libraries instead of requiring installation of MATLAB. You can choose option to download these libraries from web or add MATLAB runtime libraries with the package. After creating standalone application, you can even share this application with anyone who don't have MATLAB installed.
You can also refer to the following link for more details: