Can I use a separate 24V transformer with an Ecobee 3 and an Aube relay?
This is A-OK

Wire R and W from the relay box to Rh and W/W1 on the Ecobee, while leaving the relay's C terminal unused.  Then wire the secondary of the separate transformer to Rc and C on the Ecobee.  The Ecobee will figure all the rest out by itself, running off of the separate transformer on Rc while switching power from Rh to W to control the heat.

P.S. any standard 24VAC HVAC transformer will do here.