Well your analogy would work in the sense if they were embarrassed enough not to fight, but in the anime at a certain point Ikaruga enters a battle area in Frantic Mode. Now we're all aware Frantic Mode just strips the girls of their outfit and leaves them in their bra and panties right? Well in this particular case Ikaruga was going completely commando under her outfit and therefore was naked. When she realized this she was extremely embarrassed, and couldn't fight, but eventually got up the courage to begin fighting, as it was either that or be killed.

So I do think that the girls would be either extremely agitated or embarrassed (depending on which it happened to), but would eventually fight the goose, and get their clothes back. I don't say this in the sense of it's what I think, but rather say this in the sense of knowing as some dialog in the games, and spoken lines by various characters in both seasons of the anime seem to suggest indifference to nudity for the most part. If you watched both including the first seasons OVAs then it is sprinkled throughout, and even shows this indifference by the way of the girls actions regarding certain things that could expose them completely. So as opposed to the games, the anime definitely shows the indifference to nudity on the girls part.

For references as to where this is suggested and the above battle happens then they are below. I intentionally left the battle description above vague as not to spoil it if you haven't watched Senran Kagura Shinovi Masters Tokyo Yoma-Hen. However the anime is the reference for it. The rest are listed below, and are being noted, cause if I'm thinking the way you are then the mindset is that certain characters are potentially more bashful about their nudity which is true, but they overcome it or show indifference to it in what I'm referencing.

Senran Kagura Estival Versus – Festival Eve Full of Swimsuits (2015 OVA)

Senran Kagura Ninja Flash OVA episode 02 "Protect Hibari's Naked Body!"

The one reference that shows both the bashfulness and indifference is mainly Senran Kagura Estival Versus – Festival Eve Full of Swimsuits (2015 OVA) as what happens in there involves each of them becoming naked in it. It's not explicit nudity but if you watch and see for yourself then you get the idea.