Hello Aspirant,

No, it is not necessary to be enrolled in a school for appearing in improvement examination.

NIOS (National Institute of Open Schooling) provides this facility to directly register with the board of education and appear for the examination on respective date.

For more information you can visit the official website.

Link :- NIOS (https://www.nios.ac.in/)

Hope this cleared your doubt.

Good Luck!!