Terminator and Matrix couldn't be connected, if only for the fact that Skynet didn't want to enslave humanity - it wanted to *destroy* it.
Unlike the Matrix, where the machines lived off the energy generated by human bodies and so it wouldn't have been in their best interests to let humanity die.
You could argue that as Skynet's intelligence & self-awareness increased, that it started to develop human-like emotions, such as hatred, resentment, & a desire for revenge. It always seemed to me that the machines in The Matrix were motivated by some complex sense of hatred of humans in addition to their logical goals of survival. The machines created the Matrix as a replica of Earth during the pinnacle of human civilization to mock us.
As for the Terminator timeline being a closed loop, I infinitely prefer that version. And if it hadn't been for James Cameron pinning a date on Judgment Day in T2, the movies could still exist as one closed loop.