Can a non-resident even open a UAE bank account, and can it be done remotely?

Possible, but only around four to five UAE banks open accounts for non-residents, and they traditionally require you to appear in person; approvals take three weeks to six months. Expect a minimum balance near AED 30,000 (savings) plus documents like six months' statements, passport, proof of address and a reason such as your property purchase. Some brokers help arrange it.