Not input per se, but they can see what sites you visit and apps installed. Getting every keypress is a bit harder to my knowledge. Depending on mobile device management (MDM) software used, they can have granular access to running and installed apps, web traffic logs, and access to memory in an aim to control corporate data. Also, most MDMs running on non-corporate (BYOD) devices run corporate data in a sandbox that is managed by the MDM separately. If you have a corporate phone, than this is usually not true and the MDM can see much more data.
Now, the question of will anyone look at what you wrote is a bit harder to answer and it depends on the size of your organization. My firm will not really look unless there is a HR or legal request or you pop up in some reporting of malicious site visits.