In that little box of household members on Ancestry Hannah does come up first but if you click on her name it says she is from schedule 153.
The next name is Annie Ivey (William's wife) but the schedule is 154, ie a new household.
On the actual image Hannah is on her own, on the previous page, living next door (164 Lynton Rd) at the same address as a Mr & Mrs Norman and the Cowderoy family. She has one room, the Norman's have 3 rooms and the Cowderoy's occupy 4 rooms.
Annie and all her children are at the top of the next page and (schedule 154) living at 166 Lynton Rd.
I think you are reading too much into the fact she is in that little box of family members!
On the image it shows Annie's widowed mother, Catherine Hocking (written as mother in law) is living with them, but she doesn't appear in the little box!
I think Hannah Rose being in that box is just a mistake on Ancestry's part.
But certainly, the only way to be sure is to get James' birth certificate.