Does InstallBuilder support component selection?

Yes. To specify different components, you have to add <allowComponentSelection>1</allowComponentSelection> to your project.xml. Then, you can add different components inside the componentList section of your installer project file. The components defined will be shown to the user. For example, you may use:

<componentList>
       <component>
           <name>default</name>
           <description>My Application</description>
           <canBeEdited>1</canBeEdited>
           <detailedDescription>My application detailed description 
           </detailedDescription>
           <selected>1</selected>
           <show>1</show>
           <folderList>
                   .....
           </folderList>
        </component>

        <component>
           <name>database</name>
           <description>Database application</description>
           <canBeEdited>1</canBeEdited>
           <detailedDescription>Detailed database description
           </detailedDescription>
           <selected>0</selected>
           <show>1</show>
           <folderList>
              ......
           </folderList>
        </component>
 </componentList>