I need to create a circular array of leds somewhat similar to the NeoPixel Ring from Adafruit. Is fritzing capable of this?
Yep, select the partyou want in pcb view by clicking on it and in inspector (lower right window) change the rotation field to the angle you desire and you should be away.
Also while in PCB view if you mouse over the corner of the part (imagine it is a square even if it is round) you will see a small curved arrow appear. It will allow you to drag and turn the part.