You CAN break it, but @warpchy is right about not being able to use cards that reference “rezzed”. From FAQ:
• When encountering an Archangel during access, the Runner
follows timing step 3 of a run, ignoring the portions about
approaching ice/the server.
• If Archangel is encountered while accessed and it is moved
from its position as determined when accessed (e.g., from
R&D being shuffled during the encounter or from Archangel
being trashed from HQ by Utopia Shard during the
encounter), then the encounter immediately ends and any
currently open paid ability windows close.
• Archangel is not considered to be rezzed during its
encounter, and cards that interact with rezzed cards, e.g.,
Datasucker, cannot affect it.
You see, the FAQ says we encounter it as if we are in Step 3 of a Run. We break in 3.1. You can break the Angel.