Not exactly. In the beginning, Starfleet didn't know what had happened to the E-C. In the end, Starfleet did, as later evidenced by "Redemption". Yar's antics in the past apparently made a small but significant difference after all.The timeline at the end of the episode is the same one as the timeline at the beginning of it.
The only reason Starfleet found out in "Redemption" is because of Sela. There's no evidence that Sela did not exist before YE.
Great episode
I also noted that a lot of crew in that alternate universe also wore the uniform from seasons one and two.
At first, the 'new' uniform (the one with the collar) was only used for senior officers. Junior officers continued to wear the one without the collar. Eventually this was phased out completely.