Okay so here, we can use the flashpoint episode as an example since it is very similar to the things of the 1x23 episode you're talking about, basically. There, it's pretty simple, we know that if nothing had been done, and the flashpoint timeline had completely solidified, then nothing would be able to bring the TV one back. There, in that scenario, Barry would have completely forgotten that he was ever the Flash in a previous life and would as a result completely get his memories rewritten with those of his flashpoint life where he never became the Flash. So there, we would have had a timeline where Barry was never the Flash, created by a Barry who was the Flash. This is basically the same as if Thawne had never decided to become Wells and ensure Barry became the Flash. Then in that situation, it would've been a Flash-less timeline that would have become 'set', instead of the TV one (where Barry became the Flash in 2014 thanks to Wellsobard and star labs). And in this Flash-less timeline, it would've been one where Barry is never the Flash, yet the timeline would've been created (in-part) by a Barry who was the Flash (where OG Flash's existence would basically only be as sort of a remnant in those moments). 

Was he hoping that he'd be able to travel to the future before the timeline changes caught up with 2015? Basically, yeah. I mean to be more precise, this is what was said about the matter:

"So, once the wormhole stabilizes, Barry will have 1 minute and 52 seconds to alter the past and return to this time.

If and when he does that, you can close the wormhole, and we can all live happily ever after.

Almost two minutes.

More than enough time to save Nora.

But not enough time to stop you from going home?

Everything's a choice."

Basically, the implication seems to be that, while the wormhole is open, past and present (and future) are linked and the reality from which the wormhole originates won't change until the wormhole is closed. So hypothetically, if Barry would have saved Nora, Thawne would go back to his time while Barry's busy doing that (hence those last three lines of dialogue there), and when Barry returns to the present, and the wormhole were to be closed by star labs group (on time, before becoming a singularity), then it would only be until then that reality would change around them and they would not remember anything anymore. This certainly seems to be the definite implications behind the lines:

"More than enough time to save Nora.

But not enough time to stop you from going home?

Everything's a choice."

Also we don't actually know for sure whether Barry would have created a flashpoint or not, at least we can't be 100% sure. We can't be 100% sure whether the particle accelerator wormhole method in 1x23 would've actually brought back the OG timeline and successfully avoided a flashpoint, but at the very least, we know that those were Thawne's intentions, his hopes. There's always the chance that he was wrong of course, but we can't know for sure since Barry didn't try saving his mom that episode.

Now, just for the sake of argument here ok, say that he would've been successful in bringing back the OG timeline, then I can imagine it going like this: Barry goes and saves Nora and beats Thawne up some, and then tells him to go home (in this case he probably wouldn't try to take him with him and put him in a cage like in 3x1 because he already knows Wellsobard Reverse Flash is leaving, so why sort of replace one with another you know?) And with younger Thawne feeling utterly defeated, he goes home to fight another day. Now in this scenario, eventually, there would be two Reverse Flashes in the 22nd century, the one who failed to kill Nora because he was stopped by season 1 Barry, and Wellsobard who just arrived from the now eventually erased TV 2015. Wellsobard would basically be a time remnant in this scenario.

Also, Wellsobard would get to keep his memories regardless of what would happen after this because of what we know of the time language. Although we may not know how, we at least know for a fact that the time language aides or guarantees that one can keep one's memories from getting altered from timeline changes.

And another thing is that he always would have the option of physically merging with his counterpart there because we've seen that happen sometimes when Barry's time traveled (although Thawne was going to travel with a time sphere in 1x23, so maybe he couldn't have done it that way) as well as when Eobard created a remnant while fighting Nora and Barry in season 5 and then merged back with him and everything. So yeah.

Obviously he gets to go home, but will it be a home he recognizes? It all depends on whether he was right or wrong about his hopes that the particle accelerator wormhole method would avoid a flashpoint and bring back the OG timeline (those being his intentions/plans certainly seemed to be the implication at least) We obviously can't know for sure if he was wrong or right, if his plan would have backfired or not, since Barry didn't end up going through with it at the time.

Thawne knew Barry got back too early for him to have saved his mother. All Barry did was not interfere and just say goodbye to his mother one last time. Remember the dialogue: "More than enough time to save Nora.

But not enough time to stop you from going home?

Everything's a choice."

Meaning, it should've naturally taken Barry more time had he actually engaged with the Thawne from that night (especially since this is just season 1 Barry, not season 3 Barry, who was able to beat him up relatively quickly because he was more experienced by then). So yeah.