There are SMPS designs which will turn on and fail to regulate with extremely light or no output load. This regulation failure results in the output going higher than intended, which can toast the output caps or feedback.
These seem rare in the "real world". Most SMPSs I've seen either have a minimal internal load (big resistor), a zener to clamp things to sensible levels, overvoltage feedback causing the supply to shut off, or are simply capable of regulating down to no load.
A SMPS that damages itself if powered with no load attached is certainly possible to design, however, and I wouldn't put it past many designs, especially the low cost "foreign" designs, to ship like that. It's always safer to just put some minimal (at least a few dozen mA) load on the supply.
As for the OP, the "power supply" you seem to be referring to is probably just an isolation transformer. It could be fatal for your monitor (likely so) to hook it directly up to AC mains without this in place, but as long as you didn't do that, you shouldn't have killed your monitor. Any other symptoms being exhibited by this "dead" monitor? Is it making any noises, do you get HV (static on the front of the screen), tube neck glow (from the heaters), etc.?
The failure of the monitor may be coincidental, or you may have accidentally fed it a signal outside of it's design range. That will normally take out the HOT, which is fixable, though sometimes more than the transistor itself goes.
Being such an old monitor, there are likely some capacitors in need of replacement. Some caps can cause failure when they finally go too far from their original specs. Diagnosis of this can also be helped with symptoms, though it may be easier for you to just install (or have installed) a "cap kit".
As for discharging, just remember the 1st rule of high-voltage electronics: Thou shalt keep thy left hand in thy back pocket. If you're a leftie, replace "left" with your dominant hand.