A four unit can never generate enough revenue to get a professional management company (neither can my 20 unit honestly), so you are stuck with what you are seeing. 

When it is paid off, the place should generate ~$25K in cash flow annually, which will be a big help when I retire.

However, the property already has four tenant-occupied units, generating the income of a fourplex and has been doing so since 2005. 

Admittedly I operate in the public eye a lot more than your typical landlord or real estate investor so I'll receive a higher amount of this type of stuff then most but most if not all landlords or investors are going to face this type of stuff everyday.

I agree it’s not that great but it’s not a pure financial loss either (it would become only if you lack sufficient liquidity to operate the asset as planned over the period).

The short answer is the financing depends on many factors; income/assets and credit of all partners or parties to the transaction on the buyer's side, operating income statement for the building, deferred maintenance, occupancy all come into play.Stephanie

My question is, is it realistic to be successful operating only as a Listing Agent? 

It is not operable and is impossible to move without a tow truck.

We're told it's in mint condition, but we're estimating $5k as we'd like to install coin-operated laundry (hookups are already there) at the very least.

None of this scattershot diarrhea of the fingers, this emo pleading for spoonfeeding and aversion to actually finding things out for yourself that all too many of your generation seem to be addicted to.