Do daily operations (max, min etc) on climate model data reference different periods because of UTC? If I calculate daily accumulated precipitation or daily maximum temperature from global climate data, will I be getting statistics over different local times, because the operation uses the climate model time which is UTC?

So for example, on day N I will get the maximum temperature from 


midnight to 11:59pm in London, Dhaka, Portugal (UTC 0)
10am on day N to 9:59am on day N+1 in eastern Australia (UTC+10)
5pm on day N-1 to 4:59pm on day N in western US and Canada (UTC-7)
Yes, your understanding is correct.

(this is a really short answer because I can't think what else to say!)

I'm no expert on this type of simulation, but I suspect that any application where you care whether something happens in day 158 or day 159 is probably not an application that you want to be using a global climate model for...