Question: 

Using Delegated Access / Login As does not work with Veeva CRM Desktop. The end-user receives insufficient privileges error.

Answer:

This is currently working as designed.

Using CRM Desktop requires the following login entry points:

• Sandbox Orgs: https://test.salesforce.com/
• Production Orgs: https://login.salesforce.com/
• In either cases the MyDomain URL may be used

Related Documentation:

CRM Help Documentation: 

• CRM Desktop (Windows)