For current mainstream text generation models it doesn't really depend on where the bot is and what time of the day it is, that's kind of the whole point - their text generation process simply doesn't use the current time as a possible input factor, these models would provide the exact same result (or random picks from the exact same distribution of potential results) no matter when and where you run them.

They would be expected to answer with something matching the day/time distribution that was represented in the training data they used; like the answer to various prompts of the "current president" question is dominated by Trump, Obama and a bit of Bush and Clinton, simply because those are the presidents in the training data and the more recent events simply aren't there yet - like the many models who have no idea how to interpret the word 'Covid' simply because they have been trained on pre-2020 data even if the model was built and released later.

"I was trained on a Thursday... damn."