That's of course possible to measure in theory. I meant it as a response to "Facebook, Google and others make these tests possible in their platforms" since I haven't seen it exposed as an explicit option on either.
Then you haven't been talking to the right ad sales teams. Google and Facebook have entire product options built around this specific concept. You can run a "ghost ads" test on Google for as little as $20k in ad spend; it's relatively accessible even for smaller players.
For Facebook, Reach ads have a brand lift objective that will estimate for you. If you spend large amounts they have a measurement team that will run the actual study for you. Source: I'm running one right now for a CPG brand.