No. User Windows credentials is not supported in MultiUserEnvironment.
I am worried MultiUserEnvironment might be a wrong choice, allow me to explain:
You should not use MultiUserEnvironment unless you need to be able to log in simultaneously with multiple users. Milestone Mobile Server is an good example as many users can log in each with his own credentials. MultiUserEnvironment adds unnecessary complication if not needed. With MultiUserEnvironment being the facilitator of multiple identities it is perhaps by design that Windows current credentials are not supported.
If not using MultiUserEnvironment current Windows user is supported in general in the MIP SDK.