Does it matter if you use a lamp instead of sunlight for a plant?

It depends on the lightbulb. Regular incandescent light bulbs will not substitute for sunlight, however they do make full spectrum light bulbs (in both the regular socket style and in florescent style) that are intended to substitute for sunlight.

I've had some success overwintering my plants indoors using full spectrum bulbs but I've had just as much success using CFL's. CFLs drain less electricity, thus costing me less to have on all day (the plant still wants it's full requirement of sun; 8 hours for a full sun plant)

CFLs are also easier to find than full spectrums and, in my area cost, a little less at purchase.