The answer is possibloy, but probably not, although streptococus has been known to be transmitted by animal feces. I think the larger question is "should she be allowed to play with kittens".
Aerosolization of the bacteria, primarily through someone coughing is tha main way of catching strep.
If they don't interfere with her by reasons of allergy, there is no reason to be wary of them transmitting disease.
I hope she is feeling better.
no strep throat refers to the bacterias name streptoccocus aureus she probably got it just as a primary infection not the result of something else...if she did in fact test positive on a culture swab or blood test for strepto...