Even weak forces would be able to find out that the Library exists, if it's allied with a strong force that leaked out the info. What makes the Library able to withstand the jets?
GR-armor: No. AM fields will still destroy the magic. Magic has been amplified. Well, it's still bloody magic, so the AM field would still take it down.
Atlas: Really? Ripping through super-capital class armor with its bare hands? That's godmodding. Aegis class shield... What class-type is that?
Imgaitt: Again, no. It reinforces magic, which means... it's... magic. It doesn't change the fact that it's still magic. It would ignore Imgaitt's affects, and go straight for the magic part of it. Sure, the Imgaitt is left alone, or even destroyed, but regardless, the magic part would still be destroyed.