Doesn't work, because the version of 2007 we see on the show already includes the actions of the 815ers back in 1977. We know that because we see a picture of them from the Dharma era, and we see Richard say "I remember meeting them, and I watched them die". That proves that their actions back in 1977 are already part of the timeline.
No, we're talking about changing the timeline, not maintaining the current one. So, it does work. There's already proof of being able to change time. In the first episode with Miles with the kid. Daniel talks to Desmond in the past who suddenly remembers it in the future. He didn't remember that before.
Also, Jack, Kate, Hurley, and Sayid were not supposed to go back to 1977 originally. Yet, Daniel's mom and Jacob have helped ensure that they will. Anything they do is different than the previous time loop. Their present in the past is already rippling to the present. The picture in the Dharmaville. That's an immediate change.
So, yes, things will look consistent to a point from the point of view of the characters in the present. But, we're talking changing the timeline.