Sometimes when someone is ill they can be more susceptible to ideas that would automatically be filtered out when they are well. Mrs. Smith even mentions this (if indirectly) in chapter 17:

She always takes the right time for applying. Everybody's heart is open, you know, when they have recently escaped from severe pain, or are recovering the blessing of health, and Nurse Rooke thoroughly understands when to speak.

I think that is part of what is meant by "interesting state." Louisa may not be a poetry afficionado, but she was reasonably well educated ("school at Exeter"), and she was in no condition to engage in robust activity-- Captain Benwick (who likewise apparently had no one among the Harvilles to share ideas with) was there.

Did Benwick share with her the same poetry he discussed with Anne?

...the impassioned descriptions of hopeless agony of the other; he repeated with such tremulous feeling the various lines which imaged a broken heart, or a mind destroyed by wretchedness...

...If so, perhaps Louisa too could identify with the descriptions of suffering. And Benwick, having been supplied by Anne with the names of works of our best moralists, such collections of the finest letters, such memoirs of characters of worth and suffering, as occurred to her at the moment as calculated to rouse and fortify the mind by the highest precepts, and the strongest examples of moral and religious endurances, might be in a position to support Louisa as well.