That depends on a few settings. By deafult yes. When you reintialize a subscription it says I need a new fresh copy from a snapshot. Now it depends on how your publication is set to deliever that snapshot. There is a setting for each article for 'Action if name is in use'. This by default will drop and recreate the object. That will remove the index and all other contraints and objects asscoiated with that table (i.e. statistics,Foriegn Keys, triggers). If these objects are not part of the source table and in the setting for the article to be copied over then they will no longer exist at the source.
There are various ways to continue to have an index on a target table and not on the source. This just depends on what your enviroment is like.