Probably after the fact, but the ETA is tied to the passport, so when the passport is scanned (USA use eGates in the UK), it would be rejected, I imagine. I travel in and out routinely and I simply scan my passport and the system recognizes me.
OP, I would be curious to hear what played out. I don't think I've yet heard of what exactly happens without an ETA, though hopefully they got it via onboard WiFi since it's approved very quickly, usually.