You absolutely can do this, but I will keep my solution generic so you can implement it in various different ways.
First you will need to have a storage location where you store what activity the user has selected to launch into. You can implement this using various ways, probably the quickest would be to store it in SharedPreferences, but if you have a database already you could also store it inside your database.
Second you will need a method for the user to specify which activity they want to launch into. This could be a Setting Activity or even a means of selecting the current activity as the default.
Once you have all of this it is just a matter of putting the pieces together. You will want a new activity, LauncherActivity, this will be what you configure to be the main activity in AndroidManifest. All this activity will do, other than possibly display a splash screen, is retrieve the stored activity class with a default to fall back on, and launch the intent to start the actual desired activity. Make sure you call finish() on the LauncherActivity after you have launched the intent.