Yes, you absolutely can use a Fannie Mae HomeStyle loan for an investment property.
You will still need to meet the borrower requirements for a Fannie Mae investment property. Meaning, you will need to have the minimum down, qualify for the loan, and meet the reserve requirement for an investment property.
Using the HomeStyle renovation will be the same process as if you were buying a primary residence. You will identify a property, receive contractor bids, close the loan, and begin the renovations.
You are able to use rental income to qualify from a debt-to-income standpoint.
This product allows investors to leverage their cash, and make bids on distressed properties knowing that they will be able to make the necessary repairs with a HomeStyle renovation. Investors also don't need to rely on a hard money loan for the construction or repairs,