Nah there is no hint in manga to support ur argument .....
According to manga Uzumaki are descendants of Senju(Senju + Some random clan)....!
Zetsu said that Nagato is from senju lineage which Obviously mean that Nagato is a descendant of Senju..!
Madara knw every thing abt Sage due to the info on Uchiha Tab..
According to Madara as wel as Obito Sage had 2 son's and they are the founder's of Uchiha and Senju clan's ..
If Uzumaki are direct descendants of Sage like Uchiha and Senju then they must be related to both Ucahiha as wel as senju but there is no mention of Uzumaki's beng related to Uchiha so ur argument is invalid
no honestly it doesnt make sense because uchiha + senju would have life force and eye powers, but uzumaki only have strong life force. so it seems more like uzumakis would be the ancestors of both clans, not the descendant.