No, that didn’t happen in either Terminator or T2 and they never made any others ever
The third one wasn’t horrible, they at least stuck to the basics. It just wasn’t great either.
I love the ending of the 3rd one. I think it’s one of the coolest doomsday scenes from any movie. It’s the final culmination of everything you’ve been hearing for 3 entire movies. It has finally come. They could not prevent it. Their future was written.
I also really love how the entire movie all the electronics keep glitching out in the background as Skynet is slowly spreading itself throughout the internet and gaining control of everything.