If this file is on the same filesystem as your home directory and the app uses SHFileOperation to delete it (most apps do it when dealing with user files) then the file will be sent to the Trash. If there is a confirmation dialog then you can know what will happen as like on Windows you wil be asked either if you want to sent the file to Trash or to delete it. The Trash used is the standard Freedesktop trash directory in ~/.local/share/Trash. The problem is that (at least the last time I checked) it is not supported by Gnome. To undelete a file you need to use e.g. KDE or simply manually copy the file from this directory.
