Yes You can use Remote Desktop Connection without using Internet connection withing your local area network.
First you have to enable Remote Desktop from Client which will make users connect to that computer. for that follow steps.
1. Right click my computer
2. Go to Properties
3. Go to Remote tab
4. Enable (check) both the options available there One is Allow Remote Assistant .... second is Allow users to connect ....
This will make enable users to connect computer.
Now go to Remote Connection Desktop.
That you will get either in Accessories or its sub menu Communication
Click on : Remote Desktop Connection
Now you give either PC name or IP of the pc that you wanna get connected by your pc.
Hope this will help u.