Yes and yes. 息継ぎ can be done while his face is out of the water, and the state "being out of the water" is over at the time of main verb(主節時). Thus, he couldn't do it. However, the state "息継ぎができない" still continues, so 息継ぎができない also works well. In other words, if the state "息継ぎができない" is already over, for instance he is already out of the bathtub, 息継ぎができない can't be used.
e.g.
〇まともに息継ぎができなかった士道は、バスタブの外でゼイゼイ喘いだ。
×まともに息継ぎができない士道は、バスタブの外でゼイゼイ喘いだ。
(Note that the latter can be valid in a context where he always can't do 息継ぎ, e.g., even when swimming.)