The AI will indeed beeline to Rocketry & Spaceship techs when Space Race Victory is disabled. Not only that, when Space Victory
is enabled, they will continue to build spaceship parts
even after a Space Victory is decided!
At least, such was the case in my recent game as Saladin. Catherine, Washington, and (of all people) Alexander were all ahead of me in tech, until a last-minute Internet beeline vaulted me way ahead of them. I built the Space Elevator, and had but five turns left on the final parts when, out of the blue, Catherine DOW's America. And asks me to join. I figured...what the heck? The game's won anyway.
So I queued up some military ahead of the space parts, and launched an invasion against America. Unfortunately, I accidentally let the final parts complete, thus winning a Victory...but I was so caught up in the war, I decided to play it out in overtime.
Eventually, all of America's core cities were mine, except for one in the middle which Catherine had taken. But then...what's this, a Russian Great Artist?? Yup, Cathy dropped a CULTURE BOMB which, essentially, claimed ALL the American soil I'd spent so much time conquering!!! Silly silly Cathy, will you ever learn??
[Saladin DOW's Catherine...and also Alexander, just for the heck of it.]
Ok, here's the thing. I had spies lurking in all their main cities, so I was able to see that all during the war, America, Russia & Greece KEPT BUILDING SPACE PARTS, *after* I'd launched the ship, even as I pounded their cities into dust with Modern Armor & Stealth Bombers!!!!! Poor Cathy didn't even have oil...her lesser cities were actually building Cossacks (which actually managed to kill a few of my wounded tanks left out in the open, I was quite impressed by that.)
This was vanilla civ 1.61, dunno if Warlords or any of its patches changed that.