Being new to the Unreal engine and the UDK, One may be temped to ask the question "Can I make [insert name of game/game types or genre here]", when it should be more along the lines of "How can I...".
But then all the new comers would just switch the question and it wont be much of a difference.
The Idea is when someone ask a question like this...they can be sent here to get started in exploring the Unreal universe with no previous knowledge of the sort, actually make progress, and answer their own basic questions while learning the tools.
What you may need to do.
1. Check out the Master Guide.
2. Get familiar with the tools. Searching for info, Tutorials, Just using/playing around with them.
3. Do specific tutorials. Do Basic Mapping,or Getting Started with the Unreal Development Kit (by Raven) or Creating Levels (UDN). Hourences.com for Lighting, materials, etc.
Then try An entire (very basic) UDK game (Hourences) (If its too hard do some more reading and try at a later time)
4. Do More "Advanced" tutorials. For these check the UDK documentation sticky, Hourences.com, Unreal Engine 3 Video Tutorials, Use the forum search and use www.google.com.
5. Learn the elements of the Unreal engine, the UDK, 3D modeling/designing and what they do and how they are used. (Using steps 1 to 4 you should be able to make test maps and actors, import media and resources that you can edit, learn from and mess around with in the UDK)
6. Now you may be able the create a theory on how these elements can be used to bring your vision to life. Knowing what your tools are, what "raw materials" you can use and how they can be used together then can you only know what is possible.
Mods and Admins, delete if posted already somewhere, or unnecessary, feel free to modify. If it is useful I will try to clean it up and try to keep it updated. (will do a better detailed one soon...if its a good idea >__>..is it?)