A typical HVAC transformer supplies 40 VA, 1.7A at 24V, so your relay coil should probably pull a max current of 0.2A or so in order that it doesn't significantly load down the existing transformer.
When I added an Aprilaire 760 to my '82 furnace I was surprised to find that the humidifier solenoid valve was working on 17 vac, down from the nominal 24 vac. I would have said that the humidifier's transformer was being overloaded but the thing has worked now for years.
When you get your system working, make voltage and current measurements so you have troubleshooting data for when you'll need it.
Last edited by Wuzzat?; 11-07-2012 at 08:36 PM.