No.
Or at least that's what Aaron-2 and Aaron-3 believe. Aaron-3 (white jumper Aaron) is the third and last iteration of Aaron we see in the film, and he is the one who resolved the Thomas Granger paradox / comatose situation during the night of Robert's birthday party (Monday) involving Rachel and Rachel's ex-boyfriend (the gunman). The whole reason that Aaron-2 and Aaron-3 went back in time in the first place was to resolve the Thomas Granger situation.
Aaron-2 (hooded Aaron, the narrator): I can tell you with certainty what I did that night when it was my turn.
But I think it would do little good, because what the world remembers, the actuality, the last revision is what counts, apparently.
So how many times did it take Aaron as he cycled through the same conversations lip-synching trivia over and over?
How many times would it take before he got it right? Three? Four? Twenty?
I've decided to believe that only one more would have done it.
I can almost sleep at night if there is only one more.
Slowly and methodically, he reverse-engineered a perfect moment.
He took from his surroundings what was needed and made of it something more.
And once the details had been successfully navigated there would be nothing left to do but wait for the conflict.
Maybe the obligatory last-minute moral debate until the noise of the room escalates into panic and background screams as the gunman walks in.
And eventually he must have got it perfect and it must have been beautiful with all the praise and adoration he had coming.
He had probably saved lives, after all.
Who knows what would have happened if he hadn't been there?
Based on the above narration (where Aaron-2 talks about Aaron-3), while we see multiple timelines in the film, there is only one timeline and only the last revision "counts." Even if different timelines are apparently shown in the film, some of those scenes are just earlier iterations/loops. In the Primer universe, the timeline could be modified in a later iteration.
To resolve the Thomas Granger paradox situation, Aaron-3 attempted and succeeded to get Rachel's ex-boyfriend arrested and sent to jail on the night of Robert's birthday party. Aaron-2 also surmises (because he already left town when Aaron-3 was at the party) that Aaron-3 could have attempted many times to resolve the situation and that "eventually he [Aaron-3] must have gotten it perfect."
This most likely resolves the whole Thomas Granger paradox / comatose situation, preventing Thomas from going back in time in a later iteration, since Aaron-3 was now planning to leave the country the next day (Tuesday), instead of going back in time again and doing another loop to attempt to resolve the situation.
Is it possible that them finding Granger is the event that will eventually lead him to be sent back?
How and why Thomas Granger came back was deliberately made vague in the film. According to an interview with Shane Carruth (Primer writer and director, and the actor who played Aaron) (emphasis mine):
Does everything add up, or did you deliberately leave a few loose ends?
Shane Carruth: It’s never tidily summed up, but I’ve made sure the information is there. Almost every detail, from who the narrator is to how many Aarons there are in the end. But there’s one piece of information that isn’t, and that has to do with [potential funder] Granger coming back and how he was able to. That’s purposely vague. Abe and Aaron each have a point in the film where they find themselves in someone else’s past, and they both react a little differently to it. This is Abe’s moment. This man has found out about the machine and he’s used it to come back, but they don’t know from what point in the future or who told him about it. That’s what spurs Abe to reboot the whole thing, that’s how he reacts—let’s redo everything and then I’m the one in control. It was important that the audience be in the same place that they are—there isn’t any way to know. That’s the one big question that comes up, and I’m satisfied by that—that’s supposed to be the big question. I stuck with the rule that we were going to be with Abe, that we were going to see his experience. Although the narration is coming from Aaron, we only know about Aaron’s experience from voiceover and flashback material, mainly because there was no way to tell a story from multiple points of view dealing with multiple histories.
Source: "A Primer Primer", The Village Voice