We literally see how Saeki's precog works in the manga - she gets actual vision and sounds when she tries to precog. It was accurate enough for the Guardians to work out the location she was seeing. More than just a sensation or vague "feeling" (like Amu would apparently get with her rank 1 Precognition, which means by quest standards she's got at least level 2 in Precog).
The fact that precognition in this quest is inherently unreliable is because this is a quest - in Shugo Chara canon, it works just fine. The fact that Tsukasa's works better is beside the point.
My point is more that her precog isn't reliable, and that saying it is / Amu trying to say that it is, would be a lie.
And we've covered Amu's ability to lie to Midori already.
If Midori doesn't get everything she wants from Saeki, she's just going to turn back to Amu.
At which point, why didn't we just tell her it all to start with?
If we are going to call in precog support, we should go for the best precog available. There's no point in half-arsing it if we are going to involve other adults anyway.
Though, to be honest, if we are going to call in actual adult help, I would be voting for calling JPs / Hotsuin, not Saeki or Tsukasa. He's in a position to actually help with official resources and likely has the connections needed to bring the Scavengers in from the cold.
No, this plan works on the base assumption that Saeki is someone Midori respects enough to listen to at all and can distract Midori enough that she switches targets to try and pull information out of her instead of continuing to grill Amu. Her primary role is to be a circuit breaker for the conversation - the only one I can think of that Midori might be willing to hear out in any capacity at the moment, who has a decent chance of not siding with Midori herself.
Whether she can actually convince Midori to back off is actually pretty irrelevant.
Anything Midori learns about the Scavengers from Saeki is also not Amu's fault and would not break any promises made.
Sending someone to seek out information on someone you promised not tell about may
technically not be breaking the promise, but the Scavangers are not going to see it that way. They aren't Fae.
And Amu, as mentioned, also isn't a Fae.
Technically not breaking her word is meaningless, it still involves pissing off / betraying the people who she promised not to reveal anything about.
But also, as previously mentioned, the promise was dumb to start with, and the Scavengers don't seem to have an end plan beyond "Continue killing government employees".
Considering JPs is
also part of the government, if the Scavengers manage the extremely slim chance of succeeding in their plan, they will be getting ganked by demon summoning JP agents the next day, because they will be, in the eyes of the people in power, serial killing terrorists.
If they manage to win against trained combat operatives with demons, then Hotsuin will likely get involved directly, at which point they become smears on the nearest surface.
There is not a good end for the Scavengers, walking their current path, unless they plan on leaving the country and fleeing to another continent on the backs of their UMI abilities. And even that I have doubts about.
However much or little she decides to rant at Saeki during their chat, we will also then have gotten her reading on whether it is safe to bring Midori to the Scavengers' property.
If the answer is yes, we can then avoid directly spilling anything by getting Midori to talk to the Scavengers directly.
If the answer is no, we will probably get an interrupt, where we can then opt to fully disclose everything on account of the now-known danger. Or just continue to try what everyone insists on trying right now and half-ass an explanation, fail and have Midori dig out the truth anyway.
There's basically nothing to lose, except perhaps making Saeki curious, and everything to gain.
I've mostly covered this in the rest of the post, but the loss is breaking the promise anyway, in spirit, and involving an adult whose visions can't be trusted.
Saeki doesn't seem more useful than just, you know, walking within two blocks of the building and doing a mental scan for the Scavengers.
That doesn't cost anything, so in the spirit you've expressed of yes/no, that seems like a better question/test to do first?
Tell Midori what she wants to know, because assuming Saeki's ability works, she will know it anyway / ask us again, and then go do the lowest cost checking measure.
Once that is done, we can know if going into their home is actually a useful action, and
then talk about what precog support / allies are best to be called on to help with said action.
EDIT:
@Baughn Considering Amu has been in Kana's head, can we get a check on how much she thinks 'technically' not breaking the promise is going to be worth to Kana & co. ?