It is highly unlikely that Princess Nell's action would have threatened the Drummers. As you described, they ascended the extensive tunnel system upward to reach the extreme capillaries nearest the surface, which were earlier described thusly (emphasis mine):
Just as the waves were coming up into his face, his feet contacted
something hard and smooth that gave way beneath him. He was sucked
downward as the water plunged into a subterranean void. A hatch
slammed shut above his head, and suddenly he was breathing air again.
The light was silver. He was sitting in water up to his chest, but
it rapidly drained away, drawn off by some kind of pumping system,
and then he found himself looking down a long silvery tunnel.
The small fingerling tunnels are designed to have openings, and designed to pump water out if it came in. It's impossible to believe it wouldn't be resilient enough to handle accidental or intentional cuts, given that these sort of tunnels are routinely used and not just a Drummer thing:
Hackworth had been in a few of these, normally in more industrial settings. The entrance was dug into the beach, but the rest of it was a floating tunnel, a tube full of air, moored to the bottom. It was a cheap way to make space; the Nipponese used these things as sleeping quarters for foreign guest workers.
