Can a reanimated Rinnegan user use the Outer Path to revive someone?
The reanimated Nagato can use the Outer Path to revive someone. Kabuto was even planning to make use of this to capture Naruto and Bee, without letting Tobi know. 

Chapter 551 shows that Kabuto's plan was to have Nagato temporarily kill Naruto and Bee by pulling their souls with Ningendo (Human Path), then hide their souls and bodies with the Jigokudo (Naraka Path), have Nagato come to Kabuto's hideout, where he can revive them using the Outer Path. (See image below.)

He doesn't use it on Madara, because he won't be able to control Madara if revived through Edo Tensei, as you mentioned.