No, you do not "Absolutely" require a trust between domains, but there are limitations to the functionality should one not be in place, ie, Migration of SID History is impossible without a trust.
If Trusts Are Not Established
When deciding whether to establish trusts, remember that if no trusts are established, the following restrictions apply:
-You will not be able to use a single administrative account for migration.
-You will have to switch users and resources at the same time. This means that when a user starts using its target account (normally, when the user's workstation is moved to the target domain), all resources must be updated, so that the target user has the same access to the resources as the corresponding source user.
-When working with remote Exchange servers, console establishes net use connections automatically; thus no trusts between the console machine where Migration Manager is installed and all Exchange servers where the synchronization agents are installed are needed. However if a net use connection between the console machine and remote Exchange server was already established using different account, you may need to manage this connection manually.
-The computer on which Migration Manager is installed must be a member of the domain in which Windows 2000 or Windows Server 2003-based Exchange cluster servers reside. If you have Windows 2000 or Windows Server 2003-based cluster servers in both the source and target domains, you need trusts to be established between the domains.
-If you migrate Exchange first and set the source user’s account to be the Associated External Account for the corresponding Exchange mailbox, users will not be able to log on to the target mailboxes with their source accounts.
-Users will have to specify the target security account when they are switched to the target server. Because there are no trusts, their source accounts will not have permissions for the target mailboxes.