More power uses more fuel all things being equal, volumetric efficiency measures how much air you fit on the cylinder vs how big the cylinder is, however, this is only at full throttle, and you won't achieve 100% with a mild street/towing build. Also, this doesn't account for fuel consumption.
However, you can create a more efficient engine that uses less lb/hr/HP with the correct components. Many engines use .5 lb/hr/HP, and a really well race tuned engine can go under .40, well into the .3s for lb/hr/HP. When I went from a 355 SBC to a stroker 489 BBC I dropped only 1 MPG despite the fact that all the friction had increased do to the larger bores, increased stroke, higher rod angle, etc. Then I put efi on it and gained more than that back and I was doing better than the old SBC. Then I put a 3000 stall converter in it and killed it because it slips 400 RPM driving that wall down the freeway.
I guess my point is, it's possible to make more power with less fuel, but that completely depends on the components and tuning. So it could go either way. Many things effect the lb/hr/HP, including the combustion chamber, piston shape, compression ratio, camshaft, piston rings, bearing speed, intake manifold, cylinder head ports, induction (EFI?), ignition timing, etc.