The one thing this world lacks is people who actually use common sense, people seem to find the most difficult ways of doing things when common sense would work.
If you look at things and study them before you leap into them you can put common sense to work for you.
Diapers absorb many liquids, not just urine, so I can't see how people could reproduce with diapers anyhow. I mean, if they can't make it through latex then how would seaman make it through SAP and wood pulp? It's just ludicrous!
Seriously, though, I think the original question is whether diapers reduce sperm count, not whether they can be used as an elaborate contraceptive.
From what I've read, increased temperatures down below (from wearing think undies or diapers) has been shown to reduce sperm production. I found this article on the BBC (although a disposable manufacturer disputes the findings):
BBC News | HEALTH | Nappy 'link to infertility'
Diapers can't reduce sperm count THAT much, since incontinent people obviously do start families.