Yes, because for each insertion, update, or deletion, the database engine must not only modify the table itself, but also change any index that is affected by the action.
The extent of this effect, of course, depends on the index (how wide it is, regardless of whether it is clustered or non-clustered, how many disk IOs are required to update the index, etc.
Because of this, indexes should be added sparingly and, with the exception of some obvious cases (primary keys / unique constraints, etc.), only when there is a performance problem (or can be reliably predicted).
source share