Is it a bad idea to take EDI onto the Geth Cruiser?
Solution 1:
No, it is totally fine. I took her with me and she experienced no negative effects from being in close proximity to the Geth.
Solution 2:
EDI's squadmate body is remote controlled. If that body is gone, she doesn't die. She can only get killed (nonfunctional) if her quantum "blue box" on the Normandy is destroyed.
That said, she had some story difficulties, but no matter what happens, you can't lose her loyalty.