I have never tried, but I can think of at least two issues using LEDs as light-sources in a contact printing box:
The actual light source(s) in an LED module are very small points, whereas a fluorescent tube glows more or less uniformly from the entire surface. To ensure even illumination, you would probably need a rather sophisticated diffusor design if using LEDs as a light source.
Many alternative printing emulsions are only sensitive to ultraviolet or near-ultraviolet light (wavelengths below 400nm). Even regular fluorescent tubes emit enough energy in this area of the spectrum to cause the emulsion to react. White, high-power LEDs have almost no emission below 450nm and will probably not be able to expose most alternative emulsions. You can of course buy dedicated UV LEDs, but these are quite expensive and have a relatively low luminous flux.