See, that might work from the computer's side. However, that raises a few problems: Why send the weaker of the Terminators to kill him in the womb? Why not send the 1000 or the T-X since you could erase all of his influence. But, it definitely couldn't work from the humans side. The time machine was destroyed after Reese went through it. That's set in canon. But, even if we assume Reese was lying, or didn't know the truth (God, I hope SCC doesn't go down a route like that) and others went from that timeline, once again, why wouldn't they send one of the Arnie Terminators to protect him in the womb? It also doesn't work, because the T-850 in part 3 says that he is the one who kills John before being captured and reprogrammed.
My take is that the whole thing is an infinite loop. Skynet and the Resistance each send a soldier into the past in T1. Skynet cannot kill John, but enough is altered to change the future, thus destroying the timeline Reese came from. In the new timeline, Skynet once again has the idea to kill John in the past. This time, it doesn't have any knowledge of John's birth or location so it sends a Terminator to an approximate time when it does have a computer record of John (i.e. when his mother is hospitalized and he is inserted into the foster home - there would have been government files detailing this - Skynet was a government project so would probably be able to access this info). Good Terminator and T-1000 change enough of the past to restart this loop leading to T-3 and then the series, et al.