Yeah, I agree that King's Landing was of the utmost strategic importance.
However, in season three of the show (I do not know to what extent that goes for the novel), Cersei admits to Tyrion that without the wildfire, King's Landing would have been overrun before Tywin and the Tyrells arrived, and this does seem to be the case, since the wildfire did massive damage and Stannis forces had reached the keep (and was on the brink of overrunning the last pocket of resistance) by the time help arrived even with the reduced force.
The question is if he would have enough forces to fortify himself within the city. There would probably not be time, but other than that, I guess it would depend on how much of the walls had been broken. I have no real idea how large the arriving Lannister/Tyrell force was, compared to what Stannis might have had left, but from what I understand, I think Stannis had the largest host in Seven Kingdoms at the start of the battle (the defenders of King's Landing were by a very large margin inferior on their own), so without the wildfire, he may still have had enough forces left to repel the new arrivals.
However, Stannis would have been able to grab Joffrey, Cersei and any supporter of the Lannister family. Whether Stannis would simply execute them or keep them as a bargaining chip in an attempt to make Tywin back off, I am not sure. I know Stannis is rigid when it comes to justice (as he sees it, and he is technically right), so he would probably name these people traitors and simply have them executed.
Except for Myrcella, the Lannister's would be out of claimants to the throne (like her siblings, she isn't a legitimate claimant, but the public doesn't know that). Victory after that (if it happened) would not bring back the dead to the Lannisters.
Again, I do not know how many men Stannis had compared to Tywin and the Tyrells, but Stannis would score a major victory even if he just succeeded in wiping out Lannister throne claimants and supporters. That is my take on it, anyway.
Edit: I just checked
this. Based on numbers (I am unsure whether Stannis' 20000 men was before or after the wildfire), I guess the arriving Lannister-Tyrell host would still have defeated Stannis. Of course, numbers are not everything, if Stannis could fortify himself in the city. And he would have a hostage that Tywin could ill afford to lose.