Yes, as long as your debt to income ratio could handle both. Lenders would want to see leases and 12 months of income from the property.
To add on to what @Rick Momsen has said. You can only do one owner occupied loan within that time frame. You can also buy the rental at the same time, however the lender needs to know about both applications and the net results to the debt ratio. As far as rental income, you will either get a copy of the existing lease agreement or if vacant, the appraiser will do a rental comp analysis and determine the likely rental income each unit will provide?
The lender will take the rents from the leases or the appraisal X.75% minus your PITI and if its a positive number, add it to your income or if its a negative number, add it to your debts. The rental typically wont add much or any to your debt ratio, because its offset by the rents. You don't need 12 months rental income from the property......it can be vacant and you can still count rents as shown on the appraisal.
I hope that helps?