"If this mortgage is put on the house within 30 days of purchase, can it be considered as mortgage debt used to acquire the home and thus be deductible?"

Uh, no. Mortgages are not deductible. And taking money from their IRA, even if they won't have an early distribution penalty, and won't have any withholding, is very risky, given they have a limited timeframe to make this happen.

They should get pre-qualified. That's the same as All Cash. All Cash simply means the Seller won't need to carry any debt or wait for settlement.

Sheesh. The ideas people come up with are amazing.