I wouldn't be worried about how long it takes. You're not going to be able to make much use of it in the next few months anyway. Seems a strange time to apply for something you can't actually use.
Actually, it seems the perfect time to apply for something that will take 2-3 months before approved and in place.... Eventually , my guess is July/August, business travel will resume. Hopefully my ABTC will be in place by then. If I waited till Aug to apply, the card wouldn’t be in place until Oct/Nov.