It is possible. There are many ways to implement.
You can push and remove by GPO, you can use a software delivery tool to manage applications by user, you can use a virtual desktop assigned to a user with that users applications or you can use application virtualization.
Assuming you need to keep track of application licensing and cannot have applications installed more times than you have licenses, I would recommend the virtualized application or virtualized desktop route. The overhead to maintain will be lower and the impact to the user will be less.
Using GPOs or software delivery will impact a user when they initially log into a machine. If licensing is a major concern, you may be removing applications on logout which means they must be delivered every time someone logs in, a major impact to users waiting to start working.
For application virtualization you can stream applications as required or catch all the virtualized applications locally and turning them on for specific users. You may want to install basic applications locally and virtualize other applications instead of virtualizing all applications. Some applications do not virtualize well. The advantage is you keep positive control over licensing as you have a list of everyone authorized to run each application.
Use of a virtualized desktop environment can be a better alternative. With the ability to check out a desktop you can control the virtual desktop and potentially leave the host system as user owned computer. You could redirect user profile (and files) to a network location. You need an application delivery mechanism to populate the applications for the initial desktop or create desktop templates with application sets and assigned as required. Note that not all applications can be included in the prepared image template and must be installed post activation.
They all depend on specifics of your situation, environment and cost. Don’t forget the cost of maintaining and patching applications.
Virtualized environments are never cheaper than other environments with larger up from costs. What they provide are positive control over access; better management of licensing, versioning and patching; and flexibility.