if the trust is two way, then it will definitely work
Otherwise if the EV Server (such as EVServer.DomainA.com) cannot authenticate DOMAINB\User then it will give an access denied to the user, and a logon failure will be put in the Event logs.

If there is only a one way trust from the users domain to the EV domain, and the EV cannot authenticate, the only for it to work is if the user enters teh credentials of a user in DOMAINA where EV resides.

The type of event you will see for the Authenitcation failure would be this

Event Type:             Failure Audit
Event Source:          Security
Event Category:       Logon/Logoff
Event ID:  529
Date: 2/13/2012
Time: 12:18:16 PM
User: NT AUTHORITY\SYSTEM
Computer: EVSERVER1

Description:

Logon Failure:
 Reason: Unknown user name or bad password
        User Name: myUser
        Domain: DomainB
        Logon Type: 3
        Logon Process: NtLmSsp
        Authentication Package: NTLM
        Workstation Name: win7Machine
        Caller User Name:  -
        Caller Domain:        -
        Caller Logon ID:       -
        Caller Process ID:    -
        Transited Services: -
        Source Network Address: 192.168.100.10
        Source Port:            1999