If that were the case. Then if Naruto got sharingan, he'd have rinnegan in a few years. Higher chance of that than tenseigan for Naruto imo.
Sasuke doesn't need tenseigan tbh.
It's more of a Hamura thing. Hinata has a better chance, in fairness :L
Edit: Thought about it a bit. Not a chance for Sauce. Hamura got the byakugan genes etc. Hago got the rinnegan. Indra got the Sharingan. Ashura got the bod. Totally different lines. You can't justify it just because "They're both eye things." The dominant genes were depicted clearly in their respective lines. It'd take some major DNA mutation (and not in a good way) for anyone in Sasuke's line, even, to get anything similar to the byakugan since the sharingan is superior in general. May happen eventually due to fodder-Uchiha integration.
You can climb back up to your ancestors line genes/power by adding the required genes from when your line was split like Madara getting Hashi meat to go back up to rinnegan from sharingan but you can't branch off into different lines.
I only did biology for 2 years. That could all be bollocks XD