If we take Goku's words after he recovered from the virus at face value, he was already at his limit, so, in the best case, he would be as strong as in canon.
If, however, we consider the ROSAT scene when Goku first transforms into ASSJ/USSJ, going by my ASSJ/USSJ multipliers and Gohan's statement (USSJ Goku>=Semi Cell), SSJ Goku right before ascending was a lot stronger than his pre ROSAT self, which means he had had room to improve even without transcending the state.
In the second case, supposing that, by training by himself during the 3 years, Goku had become as strong as his ROSAT SSJ self right before ascending, he would be strong enough to easily defeat 17/18, at least in one on one fights. Of course, he'd have still got the virus.
The difference is that, with the extra power, he would be strong enough to destroy Nineteen before collapsing. Then he passes out and Vegeta shows up. Having seen Nineteen destroyed at the hands of a Super Saiyan, when Vegeta goes SSJ as well, Gero flees. Since Vegeta does not need to stop to take a senzu this time, he catches and kills Dr Gero. When Trunks appears, he realizes that those androids are not the correct ones, though everybody attributes this to history having changed and shrugs it off.
Life goes back to normal until Cell appears in Ginger. Trunks is still part of the plot, since I think he would hang around for a while before returning to his timeline. Piccolo fuses with Kami and goes to confront him. After learning about Cell's backstory the same way as in canon, Piccolo laughs and tells Cell that the Androids are no more.
Cell is in disbelief; he can sense Piccolo's power and doesn't think he could destroy both Androids at the same time. Nevertheless, he escapes in the same way as in canon. When the other Z Fighters arrive, Trunks explains that 17/18 were the androids Cell probably meant.
The following days are a race between Cell and the Z Fighters over who will find 17/18 first. However, since the Z Fighters don't know where exactly the lab is, Cell finds it first, absorbs the deactivated androids and becomes perfect. In the meantime, Goku has recovered from the virus and brought up the ROSAT idea.
For simplicity sake, let's say that Perfect Cell shows up when Vegeta/Trunks are training in the ROSAT. Goku goes to meet him with IT and tells him that he and the other Saiyans will become much stronger if he gives them a few days. Cell decides to wait and see.
When Vegeta exits ROSAT, he brainlessly goes to fight Perfect Cell, not listening to the others' advice. He loses and is saved by his son. Seeing how much stronger Vegeta/Trunks have become, Cell realizes there was truth in Goku's words, so he lets them go and announces Cell Games.
Meanwhile, in the ROSAT, Goku ascends and realizes the grade forms' weaknesses almost as soon as he has entered, so he works on his SSJ mastery longer than in canon. As a result, when he exits, there is a chance he has become SSJ2 too. Even if he hasn't, Gohan is definitely able to transform into SSJ2 at will, so he kills Cell right away.
Buu Saga/DBS events follow the 'Goku didn't die' route which I have described many times in the past.
