I am using godaddy shared windows hosting,
And i am building a new website, and it will have full text search on its SQL Server db.
My Question is, can full text search run on shared hosting? "i am asking because full text search will create files and edit"
yes - you can use full text search [ or at least i dont know hosting provider that prohibits such usage ] ... but expect complains / account shutdown [ based on 'terms of service violation' ] if update/select queries to your database take too long time to execute.
If you want to avoid complaints due to SQL server load time or have issues, you may want to consider Lucene.Net to do your search. It takes a bit more to get set up, but is worth checking out, especially if the Godaddy DB server is SQL Server 2005 (which I think is slower at FTS then 2008).