There's no guarantee that all your old data will be overwritten.
The OS may have allocated and deallocated part of the 2G for other purposes between you deleting the old file and creating the new file. So you may not be overwriting all of the sectors originally used by the old file. Some of your old sectors might now reside, unchanged, in files belonging to another task.
If security is your concern, you're better off to overwrite the file with garbage data before you delete it.
For ten years Caesar ruled with an iron hand, then with a wooden foot, and finally with a piece of string.
~ Spike Milligan