@nadia
Sure, but if Mab has been in the Winter garden the entire time since the attack, which is supposed to have happen a while ago, she just wouldn’t have had the time to sneak into Chicago for those crucial few days.
Even if she were able to leave Faerie, my point was that she would be too busy dealing with the fallout from the attack as well as the knowledge that the Adversary has taken her top 2 lieutenants away. Where would she find the time to spy on Harry enough to know about LC & then diagnose a complex issue & fix it?
Toot & Co are Wildfae. They may deal with either Summer or Winter; they
try to stay unaligned... but they also spent most of the first few books
trying not to get trapped in one of Harry'a circles. I think we can presume Mab can get anything she wants out of that crew!
We know that they regularly entered Harry's apartment, and even his lab, because they protected the cleaning-crew from the "dread beast Mister" and did general vermin-control; and Harry reflected how this was a GOOD THING because mice/rats eating some of his magical reagents would likely be a BAD THING.
So any Faerie Queen (or other potent fae) will be able to gain a full report of the inside of Harry's Place.
More likely... she could just step into the lab from the Nevernever! Lea had put up special defenses there... and Mab had personally taken over fulfilling Lea's obligations. So Mab had her own personal backdoor into Harry's lab.
As for diagnosing/fixing LC?
She's Mab. She probably knows magic to AT LEAST the same degree as any Senior Council member, and she is as strong as the entire SC combined. If I had to guess, I'd guess it would take her a bit less than 1 minute to see the problem, and a few seconds to fix it.