Yes, quite possibly.1
For tasks like web browsing and "office", your CPU and GPU load, and consequently net power consumption will be very low, most likely around 50W or even less. My Yorkfield-generation desktop with dedicated GPU (GTX650Ti) and 2 solid state disks uses 75-76W for such "mostly idle" tasks, but modern CPUs are a lot more more energy-efficient.
A 800W PSU would thus run at less than 10% of its maximal output rating. Probably closer to 5% than to 10%.
Yes, efficiency on modern PSUs has improved, and their load-efficiency graphs gain a lot steeper and have a much greater plateau than they used to have, but even certified PSUs are no panacea for loads in the single-digit percent range, let alone a cheaper PSU.
Even a very expensive 80+ "gold" or "platinum" certified PSU will not perform optimally at such low loads (the certification gives a guarantee for 20% load, not for 5%).
A computer with a weaker CPU/GPU and a weaker overall PSU (which maybe runs at 25-35% net power) may thus very well be more energy efficient and factually pull less electricity out of the wall plug.
My more recent Skylake system which has a 450W 80+ gold rated PSU idles at about 35W with integrated graphics only, and 45W with a nVidia 1060-6G, respectively (2 SSDs, 64GB RAM).
With the CPU under full load, it draws about 120W, with GPU also under maximum load, highest ever measurement was 280W. All measurements on the wall plug, thus these are overall (gross) values. 280W < 450W, no worries there. For a 800W PSU, that would be 35% of the PSU's capacity at 100% load.
One has to assume PSUs of similar quality with similar/identical efficiency certification, of course.