If I have multiple objects selected can I use scaling to make the objects closer together (without rescaling the objects)?
Yes, enable the pivot-point-align option.
This transforms the center points only.
One way to think of this is as a ferris-wheel - where each gondola stays in place, but you can rotate their locations.
Rotate: Even though you didn't ask about this, it helps to understand how the feature works.
As answered by @ideasman42, pivot point align option is a really awesome transformation tool. That coupled with Proportional Editing (Object Mode with Constant Falloff) the following transformations can be easily achieved.
Initial state of the objects
- Enable Pivot Point Align (Alt+,).
- Enable Proportional Editing (O).
- Choose Constant Falloff (Shift+O until constant falloff is displayed).
Left most object selected and scaled
Start scaling the objects and move the mouse while adjusting the proportional inflience area by scrolling the mouse wheel
Middle object selected and scaled
In this case, the objects are proportionally scaled about the middle object.