An argument can certainly be made that SOAs are completely technology independent, and that therefore Web Services are not an SOA requirement. That is especially true, since the term �Service-Oriented Architecture� existed long before Web Services surfaced. When discussing contemporary SOAs, however, it is pretty much an industry-standard expectation that you are talking about an application platform consisting (to a significant extent) of Web Services. Therefore, when we discuss SOA on this forum, I�d make the assumption that we are talking about a service-oriented architecture based on the use of Web services.
Having said all that, although vendor-technology independent, contemporary SOAs are expected to use certain open standards (that are, in turn, implemented via vendor-specific platforms). One of these standards certainly is WSDL, as this provides SOAs with a standardized interface definition format. While UDDI is becoming more common, it is not always an expected part of an SOA. Other standards worth mentioning are
SOAP, and key XML standards, such as XML Schema.
To answer the original question, a WSDL does not have to be published via a UDDI registry in order for it to be considered part of an SOA.