I just installed the Nest thermostat, I forgot to turn the breaker off everything seems to be working fine.
Is it safe to assume it is ok?
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It's "ok" in that if it works, you're probably in the clear. However, there is a high risk of letting some of the thermostat wires in the bundle touch while doing this (the wrong ones) which would cause a short/surge back to the controller board.
Luckily, most recent HVAC controllers have a fuse to protect the controller board from this exact scenario. Google your specific model number and look for the 'installation/repair' manual which will detail the specifics. In my case, it was a 3 amp blade fuse, which I actually found at a car parts store - it's not as easy to find at Home Depot or the like. Obviously, some troubleshooting in that manual you will most likely not be able to do (involving refrigerant or other things), but it will also most likely detail for you the blinks on the controller board that will help you localize the issue.
The short answer is no, it's not OK - you increased your risk of electrocution and that's never a good thing specially for a DIYer. Now that being said, everything is working and you didn't burn down your house, so you got off OK, but generally speaking, this was a bad idea.
The Nest happens to run 24V systems so there isn't too much electricity there (though you can still get zapped - car batteries are only 12V after all), but some systems are line voltage, in which case, you would have been in for a really rude surprise. In the USA this is typicall 120V but it could be over 200V in Europe or in some other systems - that could give you serious burns or even kill you!
The other risk was that you could have shorted something out and damaged the controller in your furnace; this would likely be a costly repair and left you without HVAC until it is fixed.
I come from the school that anytime you are dealing with electronics, always turn the power off. Even if you are careful with the wires you can still cause problems. Arcing a wire repeatedly will cause heat, which is the worst enemy of electronics, easily happens when wiring hot when you are making contact with the wire and the post, where it hooks up.
While some may argue that 24V or fuses might allow damage, I say do by the instructions, which I'm sure will say turn off power.
That 24VAC comes straight from a 208/240VAC --> 24VAC transformer.
This means that if you have a 60A fuse on your Air Conditioning unit from the panel-box, you can get a 60x10A @ 24VAC if you were to short the wires (or say, dip both hands in high-concentrate salt-water and touch common and positive with separate hands).
V = IR is the common arrangement of Ohm's law, but I prefer I = V / R. If you know V = 24VAC and reduced R to 0, you're left with a pipe that can deliver infinite flow. That "infinite flow" is dependent on the supply. In this case, your transformer is giving you for all intents & purposes infinite flow. 600 amps is MASSIVE (welders for instance weld around 20-24VAC at 100-300Amps).
HOPEFULLY there is a fuse somewhere in between that cuts this out in event of a short to preserve the circuit-board. But I seriously doubt there's a GFCI on that circuit to protect you, should 24VAC @ .3A go across your heart to kill you.