Why do we have tag synonyms? Do they really help? If I search for imaginary "Tag1", would its imaginary synonym "Tag2" also be searched?
Yes, they are useful. Tag synonyms are for tags that get created a lot, when they're a dupe of another tag.
For example, for every release of Ubuntu we synonymize it's code name:
Saucy -> 13.10
Raring -> 13.04
We do this because we don't need two tags for the same thing floating around.
And, yes it will provide the results when searching: