Reasons why
1) At the end of Halo, it shows a mechanical world, and if you read the books, you would know that Reach is NOT mechanical. Its actually much like Earth
2) The Ark and Reach are thousands of Light Years apart. How do I know? The Ark is outside of the Milky Way, and Reach is an Inner Colony world, closer to Earth. So in order for the Chief to go from the Ark to Reach he has to not only travel through time, but in addition travel many many many light years to get to Reach. So It is very unlikely that he time traveled.
Now a more practical explanation of the world at the end of Halo 3 (not Reach) would be Onyx. Why Onyx? Because Onyx is the "shield world" That the Forerunners would resort to if the rings has fired (as i remember). And Onyx took on a "mechanical appearance" and activated after Installation 04 was prepared to fire. So that would explain the relation between the Halo 3 world and Onyx.
So really when has Bungie EVER had time travel? And why include it at the end of Halo. And even if it WERE time travel, how would Chief had time traveled when he never even went through the portal?
Just needed to be though through some more