Check the amperage, or the wattage, on the new bulb. If it draws more than 55W/60W (standard Halogen headlight, Low/Hi), then, yes, it will drain more watts/amps from the charging system.
Add up the wattage on all of the lights, and accessories. The total should be less than the maximum output of the alternator. If it is equal to it, then you will be on the edge, and your charging system may not be able to keep your battery charged up; your regulator may die also, due to the strain of running it at its limit. If it is more than the total wattage output from the alternator, you are in trouble, as your battery will never charge, and it will eventually run out, and leave you sitting somewhere.
The other concern, is the physical size/dimensions of the H4 lamp assembly: will it fit in the existing bucket? If it does, then only the wattage is of concern. Cheers!
1979 CB750K (sold, 2012, but not forgotten)
1983 Kawasaki 440 LTD Belt Drive (sold, 2011)
1993 Kawasaki Voyager XII