I sort of doubt this. The Queen only gifted William two homes (Amner and 1A) so I question that she'd give Harry three, especially when he is renting the home in the Cotswolds.
Based on precedent it seems that non-heirs only get either a big London apartment (ala Margaret) or a big country house and a small suite of rooms in London for practical purposes (ala Anne, Andrew, and Edward). For any other accommodations, you're on your own.
Given precedent, there seems to be two reasonable scenarios for the Sussexes.
- If they plan on leasing the home in the Cotswolds long term or eventually buying a house there then they should take the big London apartment, giving them the best of both worlds
- If they don't plan on staying in the Cotswolds long term they likely pick the country house, perhaps choosing something on the Windsor estate