If it works with daylight it should work with one or two light bulbs.
I just tried setting the WB with my ExpoDisc and with a sheet of white paper. The lighting was a single Compact Flourescent bulb distance about 4.5 - 5 ft. from paper and ExpoDisc. Camera and Lens: D300 w/ 85mm f/1.4D Exposure mode: Program ISO 200 Metering mode: Matrix Exposure: w/ ExpoDisc 1/15th sec. @ f/2.0 w/ sheet of paper; 1/25th sec. @ f/3.2. Results: Good I tried it four times total. Two times with the ExpoDisc and two times with the white sheet of paper and it worked perfectly each time.
Thinking about it I pulled out my D70S which has a similar sensor though is older than your D40. I tried it with my D70S w/ Tokina 28-70mm f/2.8 Exposure mode: Program ISO 200 Focal Length: 70mm Metering mode: Matrix Exposure: w/ sheet of paper; 1/25th sec. @ f/2.8. Result: Good
Since I don't have a slow lens, I tried again with the D70S w/ Tokina 28-70mm f/2.8 Exposure mode: Aperture priority at f/5.6 ISO 200 Focal Length: 70mm Metering mode: Matrix Exposure: w/ sheet of paper; 1/4th sec. @ f/5.6. Result: Good Given my results it should work. Good Luck and Enjoy your Nikons!