I came across Terminator 2 on TV sometime last week. It was about the point where they blow up Cyberdyne, Arnold's procuring a getaway van and kneecapping cops.
I found myself wondering if John Conner remembered all this as he prepared to send the Terminator into the past. I pictured him looking at the T-800 as they send it into the time machine, remembering it standing on one leg, it swearing it will not kill anyone, maybe chuckling about all of it. "It's a birthday gift for my past self. His very own killer robot, which he won't let kill anyone. He will make it stand on one leg and teach it slang. *shakes head, chuckles*"
I'm not sure if that works with the Terminator universe's version of time travel. "Judgement Day" was apparently inevitable, any attempts to eliminate it merely postponed it. John Conner existed and was able to send Reese into the past to become John's father, which suggests a certain inevitability to that as well. It's like traveling back in time can change certain things, the future will react in response, but it's mostly details. There seem to be certain keystones that are consistent regardless*.
None of which answers the question of whether Adult John Conner would have remembered how things went before he sent the Terminator back. He'd certainly remember after he did it, which could be funny if it happened instantaneously. The T-800 has hardly disappeared and John suddenly starts laughing about his "Uncle Bob" or something. But I like the idea John had been looking forward to sending the Terminator back to protect his younger self, not only because it means Skynet is getting desperate, but because it was in some ways a really good, albeit brief, time in his life.
I don't think that's how it would be, though.
* I haven't seen Terminator: Salvation, so maybe it would force a complete change of that interpretation. I did look around a bit online, and the time travel wiki for Terminator franchise has quotes that suggest changes to the timeline won't be known until after the mission has occurred, but also there's a suggestion the timeline has a set path, and in some way, it resists Skynet's attempts to change it.