I don't think you'll be able to go this route mate! When you install a game, the game makes certain entries in the windows registry. Now, when you format windows, i 'believe' the registry also gets wiped out, thereby deleting the said entries.
What you can try though, is to backup the games before going ahead with the format. This should ensure that you don't need to re-download every game from steam again. Again, this is just my theory and members may point out if this is wrong.
If you can still access the drive you can just copy all the steam app folders and files onto your new installation.
I did this with about 100gb of games a while back, I did verify the local files on all of them, but *touch wood* about 2 years later and they still are working fine.
Re-install Windows WITHOUT formatting your hard drive. The new installation will dump your old windows files into a folder named "Windows.old". Navigate to the folder Windows.old\Users\<Old Username> and copy the contents to C:\Users\<New Username>. Merge the folders but do NOT overwrite any files.
Install Steam to the same drive/folder it was installed in originally e.g. I always install mine to "D:\Program files (x86)\Steam". Your games will re-install as required when you run them but all your savegames should be present as well.