The \b switch is not used in an IF test - it is an alternative way of generating conditional output, which might also include suppressing an empty space or line. For your purposes, it appears you need an IF test constructed along the lines of:
{IF«Acknowledgee_Additional_Addressee» = «Acknowledgee_Constituent_ID» "" "«Acknowledgee_Additional_Addressee»¶
"}

Note: The field brace pairs (i.e. '{ }') for the above example are all created in the document itself, via Ctrl-F9 (Cmd-F9 on a Mac); you can't simply type them or copy & paste them from this message. Nor is it practical to add them via any of the standard Word dialogues. Likewise, you can't type or copy & paste the chevrons (i.e. '« »') - they're part of the actual mergefields, which you can insert from the 'Insert Merge Field' dropdown. The spaces represented in the field construction are all required. Instead of the ¶ symbol, you should use a real paragraph break and delete the one that follows the field code.

__________________
Cheers,
Paul Edstein
[Fmr MS MVP - Word]