Simple answer: yes, but a little common sense and care and not overloading your breakers and you'll generally be ok.
You're likely going to get answers on both sides of this. So let's get the obvious part of the question out of the way first:
Question: ...Are there things in the home that can be damaged by shutting them off... at an AC source upstream somewhere...
Answer: Yes. For sake of answering what appears to be the core of the question, turning item(s) off by cutting power can break something - including the circuit breaker itself.
With this said, its a common practice, and it rarely breaks things, but it can. The real issues are probably three fold -
1.) transients (motors, compressors, and various other appliances or items with large capacitors or loads can essentially send a jolt of power back out to other devices on the same circuit and even beyond)
2.) current/power draw (even something as simple as a light bulb, going from no power to initial power on draws extra power for a moment when powered on, thus we have all seen an incandescent bulb burn out when you turn it on... regardless if by a wall switch or a breaker...) thus turning things on especially numerous things that were on before the breaker was turned off can cause both #1 & #2 above.
3.) Microsoft always tells you to shutdown cleanly before powering off your computer, a video projector, or an A/C conditioner, some dryers for example, all require cooldown time after their main cycle has just ran. From hard disks spinning down cleanly and memory in electronics getting cleared or cleaned up, to fans finishing their cooldown cycle, shutting these things off "cold turkey" so to speak, actually subjects them to high heat or abnormal conditions which significantly shorten their life or could pose a fire hazard.
These are extremes. So best precautions:
Dont bake or run the a/c furnace, dryer, heck, even listen for the fridge to be on an idle cycle. Turn off lights, computers, tv's etc. Turn off items that are not in use, and are not needed for the testing. Use a few cheap items like incandescent table lamps on a hard surface. This way, the most likely thing you are going to blow is a light bulb. Further, when you turn the breaker back on, its less likely to cause a surge.