Say, hypothetically, that some "supernatural" force causes giant talking stalks of broccoli to get up and start mowing your lawn for free. Is it your view that science would be inherently incapable of taking note of that event?
To put the question more seriously, as long as something has an observable effect on the real world, what's to prevent it from being reachable through scientific investigation?
Well, first thing I'd do is open up the "giant talking stalk of broccoli" to make sure the "supernatural" force inside isn't my brother-in-law.
If it's just a stalk of broccoli, I'd ask it why it's doing my lawn for free. (Better be a good answer too. The last thing we need are a bunch of communist broccoli stalks undermining free enterprise.)
To put the question more seriously, as long as something has an observable effect on the real world, what's to prevent it from being reachable through scientific investigation?
Nothing. But, unlike your example above, where you start with the assumption that the broccoli stalk is necessarily animated by "some supernatural force" before investigating the more mundane physical probabilities, science doesn't start its investigation with an assumption that there is no explanation other than the supernaturally inexplicable. If it did, not much would get explained, would it?