I doubt Goku would have a chance to flee, since whilst he has the potential to do so with Shunkan Ido, it tends to not be within his character to do so with him not thinking of such without an opportunity to collect himself. I doubt #17 or #18 would be lenient enough to give him this chance either. He also wouldn't be anywhere near as strong as his Pre-Rosat self and may very well be more or less the same as his sick self with better stamina, given he didn't have the additional threat of the enemies he'd face in 3 years to further his desire for strength.
Assuming he somehow does escape, he'd take Gohan to the Rosat. The two would oneshot the twins when emerging the next day and Goku would go to Kaio to find out where New Namek was, make Dende Earth's Kami and revive everyone. Piccolo would then merge with Kami and it wouldn't take much longer for Vegeta to achieve Super Saiyan and do two Rosat trips, this time taking a note from Goku and mastering the form rather than going for the Grades. In other words, things enter a similar status-quo as in the Boo Arc but with Goku around and the difference between he and Vegeta not great enough to influence Vegeta going Majin. That said, Dabura is killed along with Babidi (for those who believe Gohan was a SS2, Goku or Gohan training with the Z-Sword will cover that) and peace is restored. Once Beerus shows up, the only difference in Super for the first few arcs is that there's little tension when Goku arrives to confront Beerus due to Boo not being released. Goku finds out how to go SSG and everything goes the same up to the Zamasu Arc.
This is where things become questionable due to time travel and Future Trunks. Perhaps a version of Future Trunks would come to this timeline due to the divergence and difference between timelines not seeming to matter too much in how they connect. If so, things proceed as normal until the ToP, where the lack of #17's support role means Jiren narrowly beats Goku and Freeza and Universe 7 is erased. If there's still no time traveller to inform the cast on Black, Zamasu eventually brings his Zero Mortal Plan to this timeline but is stopped by Goku using the Zen-Oh button eventually.