Yes, but only at the time of his actual capture. That mosquito will have to bite the frogs tongue as soon as the frog is striking out Don't laugh, I've seen it happen
once in the frog's digestive system --the acids would kill the virus --however if the frog was "bit" it could be exposed to the virus just like any animal the misquito bit -- now as to weither it would actually get the virus /disease ? who knows?
Would we have to be bitten by said frog then for the virus to spread that way? Or would eating him raw be the problem? Neither seem to be a serious possibility to me.