Let's calculate the AmpHours the solenoid would have drawn from the battery. You didn't say what type of solenoid, but I'm guessing the power draw is similar to some of the stancor solenoids I found in the Newark catalog. Let's assume a 12 W draw. At 12 Volts this is 1 Amp of current. 1 week is 168 hours. That is a draw of 168 AmpHours. The largest Yellow Top has a reserve capacity of 120 Amp Hours. Yes, the solenoid would have drained the battery completely in 1 week.
Huh??? That would only be the case if it were a normally closed circuit OR if the circuit was switched to the closed position. A normal-open solenoid has 0 amp draw when not in use.... think about it, its just a cable at that point, thats like saying your cables are going to draw your battery down.
There are solenoids out there that are NOT normally open, but I can't think of why you would use one on a rig (without some super techy wiring).
If your theory were correct... my Warn winches solenoids (always connected but normally open) would drain my battery in under 2 days... that doesn't take into account the losses due to my dual battery realay (also normally open).
So, assuming you have a standard auto solenoid (think Ford starter solenoid), then I don't think your relay is draining the system.