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Yes, it is possible! Just use
Theme Changer. It's GREAT! It works exactly as you have described.
Make sure you follow the install instructions.
Basically:
1) Install the module as normal.
2) Find the "z_changeable_theme" theme and load it into your themes folder.
3) Set the "z_changeable_theme" as your default theme in your General Preferences.
4) Set your default and alternate themes using the Theme Changer admin interface!
Best of luck to you!