Is removable sticky invoice paper right tool for etching? Answered

In theory it would be possible but to actually remove the unwanted parts is hard.
Even with a laser there is a good chance some glue will be left on the material, messing the etching up.
I would use a dedicated product for the job, like LiquaMask - check Youtube for videos on the stuff, it might be just right for you.
Without a laser you can still cut the mask and remove the unwanted parts where you like to etch.
But depending on what you plan there might be better products out there, have you checked the masking films for circuit etching?
There is a blue UV curing one that can also be used for light sandblasting.
It is reusable unless sand blasted of course and you should be able to use glue to mount it on the parts you want to etch.

Go to any office supply store and you'll find full sheets of sticker paper. But this will not do good for etching. Any etching solution used will compromise the adhesive. Even if the paper is water resistant the glue will not hold up to harsh chemicals. If you find some that have resiliant glue that makes it just that much harder to remove the paper once your done etching.

What kind of etching do you have in mind?

I prefer to use masking vinyl (Oracal 813 in my case) for masking when etching glasses with etching cream. It's probably cheaper than this kind of paper and liquids won't seep through it. Due to being a masking vinyl it's also easier to remove.

You could still easily use this same sheet of paper, cut whatever you want out and try to etch a scrap piece and see how this works for you.