We use the salesforce SOAP and Streaming API to pull data from salesforce into our system. Given that Veeva CRM is an application built on top of the salesforce platform, I would like to know if our clients who have Veeva CRM accounts be able to pull data from it into our system using the salesforce integrations (SOAP and Streaming API) we provide?
you might want to consult http://developer.veevacrm.com/docs/
This comment seems to be relevant to your question:
Users can access the Veeva API by leveraging their existing Salesforce integrations. Users with systems such as a third-party single-sign on are able to access Salesforce and establish a persistent connection. From there, they can gather the requisite Salesforce session ID and Salesforce SOAP endpoint to make an API call to Veeva.
It also seems likely that in order to access data that is only managed by Veeva would need an additional set of code, although that is not exactly clear from the material published by Veeva on the URL above. You should also check this out: http://developer.veevacrm.com/api/MyInsightsLibrary/#myinsights-v2-0