Except when GET has side effects, one can embed the URL in an img tag and visitors would be triggering that side effect unknowingly. One can do this on most public forums. So no, users may not be aware.
What you just described is actually a web beacon [1], in which case the one that embed the URL is the user (and not the one who load the <img>). Web beacon can be used to implement useful thing like visitor counter service [2].
[1]: https://en.wikipedia.org/wiki/Web_beacon
[2]: https://www.hitwebcounter.com/