After killing the Brotherhood of Steel, does Veronica still follow you?

If I convince Veronica to leave the Brotherhood of Steel and join the Followers of the Apocalypse, and then I kill everyone of the Brotherhood, will Veronica still follow me as a companion?

I want to do either NCR missions or Legion missions to get the achievements, and I know I will have to kill the BoS. I heard that a high reputation keeps her with me, and Im already "accepted" by them, but I'm not sure and I don't want her to leave me. She is just too awesome to leave.

Solution 1:

You can totally do this. I Mr. Sandman'd everyone, and killed off most of everyone in disguise so I barely lost any reputation. After I dealt with them all, I exited the bunker (without blowing it up and still completing the 'Destroy The Brotherhood' mission by killing everyone, or at least all major characters) and Veronica was none the wiser. All was good.

Solution 2:

Veronica will leave if your BoS reputation falls below a certain value. Destroying the BoS will give you a massive reputation hit, so you will most likely fall below the reputation required for keeping Veronica.

At least the NCR quests you can do without having to kill the Brotherhood, as far as I remember.