If you store your images on the file system then you save database space and access to the images for browsers is faster because they do not need to be retrieved from the database tables.
If you backup your database you are not backing up all the images.
If you want a copy of your database for some testing or work you also need to grab a copy of the images on the disk.
The images are all named by a GUID so there is a direct relationship between the file name and the reference in the database. (So don't think you can add images directly and definitely don't rename them. You should just leave it all up to Sitefinity) But you do have to consider that the file system is now, in effect, an extension to your database and so you should treat it that way.
I don't think pushing new code will make a difference in regards to where your images are located but I couldn't say for sure as I don't know what your code looks like.