What kind of note are you using (ie rtf, markdown, etc.)?
Edit: I’ve just confirmed that when using RTF(D) the screenshot which I drop into the note is contained within the rtfd package and as such within the database. The same is true for formatted notes, in which the image is encoded. The image is not contained within markdown notes, which only point to the screenshot in a system temporary folder, which is presumably emptied on reboot. Assuming you are using markdown (which to my knowledge does not embed images by its very nature), and the temporary folder(s) containing the images are empty, then yes, they are lost.
PS images in markdown notes are cached by DT, so will under some circumstances still display after the image has been deleted from the file system; that cache is emptied on closing DT (but not on closing just the database) though, so it will be of no help to you (but could lead one to wrongly believe that the image was actually encapsulated within the note).
PPS If you are using TimeMachine or similar it is at least possible that the contents of the temporary folder might be backed up; I have just checked and found screenshots I made earlier on in my TimeMachine backup