Can this world function without farmers?

Of course not. We could become hunter-gatherers, but those practices would never support the population we have today. 

Not any more.  Eons ago, most families lived on acreage and farmed for all the food the family needed.  Now, most families live in the city or urban areas - so no acreage.  Now, we just go to the grocery stores to buy what we need to eat.

Human would die without the food that farmers produce.

We need farmers.  They are outstanding in their field.  Cave Man used to be a hunter and his wife Cave Woman was a gatherer.  Then one day Cave Woman told Cave Man she was sick of picking up nuts and had planted a garden.  She flat refused to go wandering about tither and yon. She told Cave Man he could do whatever he wanted but she was staying put whether he liked it or not.  Said she didn't need him anyway.

Theoretically, yes. Humans went a long time as hunter-gatherers until someone decided that it was more efficient to raise barley for beer-brewing than it was to travel from wild plot to plot. Also, ranchers provide food, if less efficiently than farmers do.

maybe by researchers who do same work as them

urban society could not

For about a week.

Function?  Yes.  Eat?  No.