Yes, this should be possible using Citrix's single sign-on. Without knowing everything about your environment, it is difficult to tell you the exact steps you need to take. But, you will need to enable SSO on both the desktop and server side.
The enterprise version of Citrix Receiver install SSO components by default. This component installs a GINA DLL on the workstation which intercepts the user credentials when they log in, unlock the computer, etc. You have to enable this functionality by setting some registry values in:
HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Citrix\ICA Client\Engine\Lockdown Profiles\All Regions\Lockdown\Logon\Local Credentials
Similar to:
EnableSSOnThruICAFile=true
LegacyLocalUserNameAndPassword=*
SSOnCredentialType"=Any,NT,NDS
SSOnUserSetting=true
UseLocalUserAndPassword"=true
The tells Citrix Receiver that it's OK to capture Windows credentials and pass them through to XenApp.
You can then create an .ICA file to launch the Citrix desktop, but you don't have to worry about scripting anything or passing credentials. They will be passed for you. You just have to make sure that SSO is enabled in the .ICA file as well. In the [WFClient] section add:
UseLocalUserAndPassword=On
SSOnUserSetting=On
EnableSSOnThruICAFile=On
Plus whatever other ICA settings you'll need to launch the desktop. Double-clicking this .ICA will then start the desktop with the passed through credentials.