No. A column with a large percentage of NULLs should not be indexed, because the speed of accessing these rows degrades when the value of a large percentage of rows is the same.
A composite index on the columns used as filter in the WHERE clause should be the choice.
A choice of a single-column or composite index should be considered, depending on filtering, ordering, and grouping. For the large amount of data manipulation, the index could be dropped and re-created after the INSERT,UPDATE, or DELETE jobs were done.