Re: "..how long would it take to post-process her message?"
Well, the TOS computer was still pretty primitive. You had to address it as "computer", and it always replied "working". I guess that made sense to the writers given how the mainframes of the day operated!
What is frankly ridiculous about Star Trek is that they have all this fantastic tech centuries ahead of ours (if not more, transporters will never happen) and then computers that are shittier than the ones today. Seriously, you need a helmsman to steer "evasive pattern beta nine"? Or to "lay in a course"? The computer should be flying the ship, firing weapons, and doing pretty much everything if you can have FTL travel and transporters!