Disposable diapers do expire but I think the problem was more with the old style pampers and other plastic backed diapers with the sticky tapes.
The problem with those plastic backed diapers is they'd start turning yellow and the tapes wouldn't stick as good.
The new diapers with the Velcro on them shouldn't lose their stickiness especially in only 4 years.
If you can get the diapers cheap enough then I'd go ahead and buy them.