To learn a new language

I've accepted a position at work that has me spending the majority of
my time acting as Product Owner in our Software Engineering
organization (which has adopted a mostly agile development process).
The primary team I serve as product owner for (our customer portal
team) has some of our most seasoned developers and is more or less
self sufficient. My day to day oversight of their efforts is minimal
if at all. I set priorities every two weeks, check is periodically and
answer questions as they come up - but that is pretty much it.

Having a background in software engineering is it my inclination to
learn the language we develop in (C#). I'm confident I could do it in
short span of time, but I am worried the result will end up in me
becoming too involved in our project for the team's comfort. I'm happy
to let them drive technical direction and don't want to meddle in a
team that is clearly producing, but I'm also someone who enjoys
discussing software architecture.

I recently spoke with our CTO about my progress in my new role - and
one of the things he left me with was that too often I go out of my
way to "seem like the smartest person in the room." While this isn't
something I realized outright, I do understand where he is coming
from. He suggested in places where I might be inclined to make a
declarative statement, I instead restructure my thought as a question
to drive discussion. My gut tells me his advice here is solid, but
I've always thrived in highly technical environments where challenging
one another on ideas is the norm.

I wonder how his advice would be applied to my current situation,
where learning the language might result in my inclination to start
throwing out ideas for the team to challenge.