FPGAs are a undifferentiated sea of configurable logic gates with configurable connections between them[0]; it's not quite wiring together bare transistors but it's not that far removed either. None of the elements of a von Neumann architecture are there; if a engineer wants any of those things in their design, they would have to assemble it themselves from the available gates[1]. So, no, building a design for a FPGA has little to do with programming in the sense that most people mean it.
[0] With various special function blocks interspersed at regular intervals depending on the manufacturer and model of the FPGA
[1] or buy a pre-made soft-IP core