I haven't tried that, may be working. I do use
Dawn as my dish-soap - grease cutter and it's good all by itself, don't know if vinegar would improve it.
I make my own window-cleaner: 1 cup white vinegar, 1/4 cup household ammonia and 1/4 cup alcohol, adding enough water to fill a 1 qt spray bottle, it works very well.

I've found that vinegar is an excellent grease-cutter. However, if you put it into a soapy solution, it cuts the soap (or detergent). In fact, to help keep dark colored clothing dark and lint-free, add a cup of vinegar to the final rinse. But it won't make your dish detergent more effective.

Use vinegar in a 50/50 solution with plain water to: wash windows, clean the bathroom, wipe counters and kitchen appliances; put in a spray bottle and use to swipe away fingerprints from doorknobs and light switches, and anything else that needs a spritz to clean. Use undiluted vinegar as an antiseptic cleaner (rinse after applying), especially if someone has a cold. You can use vinegar (1/4 cup in 1/2 gallon of hot water) to pre-soak greasy plates, pots and pans, but frankly, dish detergent in very hot water will usually clean just fine. It helps if you habitually use newspaper or papertowel to wipe off excess grease before washing.

Had an empty dish soap bottle. Poured in a small bottle of Ajax.+ 1 tbsp white vinegar.

Looks like a bottle of cheeze whiz. Will let youknow how it works.

Had an empty dish soap bottle. Poured in a small bootle of Ajax. Looks like a bottle of cheeze whiz. Will let youknow how it works.

I don't know about how the vinegar and soap combination may cut grease.
But when you described the combination as "cheese whiz", I got the idea that Ajax may have some sort of Sodium Chloride, Baking Soda etc...
I've used baking soda and vinegar to clean all my drains for years and we've have had very few problems with clogged drains. We're talking major fizz action here.

Pour 3 TB baking soda in the drain, add 2-3 TB vinegar, stand back........let it sit for about 15 minutes , then flush with fresh water. Repeat as needed.