In the books Varys' loyalties lie with another Targaryen that has not been introduced in the show, so I find it unlikely that in the show version he's not true to Dany.
Also I doubt Cersei would switch Tommen for Gendry, she clearly loves her children and to jeopardize his future, Jaimie's and Tommen's just to stick it up to the High Sparrow seems a too much harsh price to pay. She screwed her brother FFS, imagine the real world consequences even in our modern age if Diana Spencer's sons, William and Henry, were born of incest with her own brother. That would be too much to swallow even today, let alone in Westeros.