I have tested a small 120 vac relay directly driven from a ssr4 channel. I believe it has a coil current of around 20 mA but I have not measured it. Most smaller relays have contact current ratings from 5 to 15 amps so you can control some pretty large loads, but you could drive a much larger relay such as a contactor using the smaller relay as a 'pilot' relay if you required more capacity.
When I was considering using a relay to switch inflatables in my display, I was concerned about possibly damaging the triacs in the ssr4 or lynx due to the inductive kickback of the relay coil, but this has proven not be a factor since I setup a looping test sequence in vixen where the relay clicked on and off every 3 seconds or so and let it run for several days without any problems. However, a larger relay with more coil inductance could certainly be an issue...
Just be sure to run the channel in vixen at either full on or full off to control the relay.
I don't think driving the channel at a reduced level to achieve a lower drive voltage would be a good idea, but I haven't tried this.