Short answer: No. Assigning someone a section only opens that one section's content for them; they can see the completion status of every other section, but not what's inside, and two sections can never be assigned to anyone.
What a teammate can see
Once you assign a section to a teammate, they get view and write access to that section's content. Beyond that:
Every teammate can see the status and completion percentage of all nine sections on the dashboard, including the two you keep for yourself.
The two owner-only sections, Financials and Vision & Leadership, always show as locked to a teammate, with chips like "Only you" or "Never shared". These two sections can never be assigned to anyone, even if you try.
Shared reference lists, such as your roles list and document types list, are visible to any member. These aren't section content, just shared taxonomy used across the portal.
What a teammate cannot see
A teammate cannot open the actual content of any section you haven't assigned to them. They also can't see certain fields even inside a section they hold: for example, base salary and discretionary pay in Your Team are visible to you only, regardless of who else has access to that section.
Note: Assigning a section grants view and write together. There's no way to hand someone a section that only lets them submit answers without also letting them see what's already there.
Things to keep in mind
Tip: Assign only the sections a teammate actually needs to work on. There's no way to later narrow their access to a section without removing them from the organisation and re-inviting them.
Warning: The "assigned to [name]" label you see next to a section is temporary and tied to your current session. After a reload or on another device, that label disappears and the row shows your own avatar again, even though the teammate still has access to the section.