Mold can be lethal to seeds/seedlings if left unchecked. I germinated corn seed at one point, just to the point of root emergence, in wet paper (this was going to peat pots in the cold frame, and from there to the garden under cover, for a late May harvest).
Out of the 2 lbs of seed, about 2/3 of them developed mold just as the root began emerging. these were separated, and treated with potassium bicarbonate before planting, in the peat pots (which were then drenched with a biofungicide (Bacillus subtilis) at the first watering). I got an 85% healthy germination rate from these, which is not bad considering the conditions.
Out of the seeds that did not grow mold, I only got about a 20% germination, which I am guessing to be from mold forming after planting. Looking back I probably should have treated all the seeds against mold at the time they were planted.
Obviously this experience wasn't dealing with coffee beans, but I think it is useful experience for a lot of pre-soil germination when dealing with fungus.