Is it possible to insert that small screened opening in a glass block window if it is already installed or do I have to have the whole window removed and start over?
I'm not sure what you are asking and what you have seen to make this inquiry.
If you presently have a glass block window in your home and wish to change it or part of it and put in an operating window with a screen, I believe you would likely be wise to consider removing the entire area that is glass block. It may be possible to remove only part of the glass block and have a window custom made to fit that which you remove but it may not be as attractive or effective as the other option you have below.
I assisted another individual who wanted an operable glass block window which they saw on Bathroom Renovations, on DIY in episode DBTR-405. The link for such a window is below. You may find this site more to your liking and still have a glass block area but with an operable window which is also glass block (Vinyl Blocks). Check it out. These windows look awesome and offer some unique colours and designs as well as being fully operational.