Yes they can be bred together in captivity. Because their ranges do not overlap, you will never find an east/west hybrid in the wild.
If hybridized in captivity, either sex can be the female, as they are similarly sized snakes (though the EDB holds the record for the length and weight of Crotalus species). The father's name is listed first in the hybridization. So an east-west diamondback (C. adamanteus-atrox) would be the offspring of a male EDB and a female WDB.
I once saw a captive bred hybrid between a timber rattlesnake and an EDB. Gorgeous animal. If I recall correctly, it was listed as C. horridus-adamanteus; a timber EDB. Its father, therefore, was the timber (which makes sense, as EDBs are notably larger on average than timbers). It was bigger than both its parents, as is common for hybrids of many species.