OK I tested and this is what I worked out:
When you power down - your parts (all of them) will be as you left them.
When you change to another project and change back again - your parts will be as you left them.
When you start actively saving projects and parts things get a little more complicated.
If you actively SAVE your project you then have TWO states in stored in OT memory:
1- The SAVED project. (Which is like a snapshot of how your project was when you saved it, including parts)
2- The CURRENT state of your project, which includes any changes made after the save.
If you then also actively SAVE YOUR PARTS you will have THREE states stored in OT memory:
1- The SAVED PROJECT, including the parts
2- The SAVED PARTS, which can be different to the parts saved with the project
3- The CURRENT STATE of the project, including any changes to the parts since the last save
Any time you actively RELOAD using PROJECT > RELOAD or PART > RELOAD (which is different to just turning power on, or changing projects) you will OVERWRITE the CURRENT STATE of your project or part with the saved version.
Counterintuitively, saving parts actually makes your parts both safer AND more vulnerable. This is because the key combination (FUNCTION + CUE) to RELOAD a previously saved part, and overwrite your current part settings, is very easy to make by accident. This can’t happen if you have never saved the part (You just see “SAVE PART FIRST!” message and your part stays intact).
Merlin’s guide details a nice ‘back to base’ creative use for this quick parts reload function, and I’m not saying it’s a bad thing, just that it can be more or less useful depending on how you use the OT. Reloading a project, on the other hand, requires a menu dive. I find it useful as a snapshot backup, but of course I still get into saving parts because it’s good to have them recallable independently from the project.
Another backup method, which is easier to keep track of, is saving renamed versions of your project as you go.
But in answer to your original question - YES, saving a project saves the parts.
There are still loads of ways to mess up (!) but YES, saving a project saves the parts.