I just did a quick test. No, nothing was changed.
I opened a project, moved the form, resized the form and closed the project. I was asked to save the changes. If I answer no, then nothing is changed and there will be no new bak file nor backup folder created.
What you said is a very serious issue. If I experienced it, I would be sure to report it.
I use Lazarus 2.0.8 Linux.
-edit-
If you compile/build/run the project, all the changes will be automatically saved without asking you.
A concrete example: I use a couple machines, an old one with a with a 1024x768 screen and another with a 1366x768. Now, a project is started in the first machine with a 600x400 form at, say, (240,200) and then moved to the second machine. Since the screen is wider, you can have, for example, a wider Project inspector so you move the form a little to the right to have it fully visible and keep building the project: change some properties in the PI, add code, compile, test, rinse and repeat. Perhaps you even make the form a little wider to adjust for the wider machine...
The net result is that after all that most or all properties relating to the position (and maybe size) of the form have changed, so when you move the project back to the first machine to keep going on it, it doesn't look quite right ... much less if the machines have different DPI!
That's the "problem" and it has no easy solution since, in fact, you
changed those properties and that
has to be reflected in the form file.
I don't really mind much, there's little difference between these two (and in fact most of the other) machines, but it's easy to see what might happen if one of them had an even wider or high-dpi screen