If Stannis had taken the city before Tywin and the Tyrells arrived, would he have been able to hold it?

He’d have good odds. 10-20k men behind the walls, and the strength of his navy to open up supply line to the Stormlands and Essos and keep himself from being blockades, it would be difficult to dislodge him.

But the major thing would be the politics. Seated on the Iron Throne and with the Lannisters’ claim to the Throne dead, the other half of the Stormlands comes over to him replenishing his ranks. Suddenly Stannis is up to 30-40k men, and there’s not a lot holding the Lannister/Tyrell alliance together.