Hello Steve,
Damp ingress is symptomatic of leaking roof or other joints, A cover may prevent water getting to a leak track,but it won't cure the problem. As soon as you remove the cover and you get rained on, then you will get ingress.
If you have a water ingress problem, its far better to get it sorted propery.
Full covers are sometimes accused of causing dam, but again, the cover its self is not to blame.Damp and condensation are sympomatic of insufficent ventilation. Keep the van well ventilated and the problem goes away or is at least managable.