SQL will not overwrite existing rows because of a table's size. Look at whatever is doing the insert into the table, from SQL's side, if it's told to do an insert it will do an insert and if the database is out of space you'll get an error.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability