When Padcapping should the pad be damp to start with?

Damp is best, although since you are using a cleaning product that will eventually be removed from the carpet - either by being absorbed into the pad, or via the dried encap process - it probably doesn't make too much difference. When cleaning with a non-encap cleaner,I think the water in the pad helps the rinsing process. Although this could be counter-intuitive, since a dry pad will have greater capacity to absorb liquids. Good question. Maybe a hydrologist/physicist out there will have the definitive answer.

I've always seen it written that cotton absorbs soils and water better when already damp, and I always figured it didn't matter much with synthetics.

I like my gladiator pads damp from the spin cycle.