Based on Doc's answer I'm pretty sure I'll be fine, but just to hedge my bets, I reached out to the airline in question (Turkish). They replied promptly to request copies of my passport and the ABTC card, which I provided. A few days later, they got back to me and confirmed :
We have forwarded your document to our sales office in Ho Chi Minh City and your travel has been approved.
Since I gave them my PNR, I presume the booking has now been annotated with this approval and they can see this at check-in in Vienna. Fingers crossed!