Well, I posted basically the same question in a couple of other places, and got conflicting answers. And the information I found on web searches tended to explain HOW to set up a hierarchy, but not how it really worked, and information on synonyms is especially limited, and often conflicting. So I did some tests. So as to not use any words that were already in my keyword list, I built a simple hierarchy of words not currently in use:
Colors
Blue
{Cyan}
{Azure}
Red
Pink
Salmon
Rose
Green
{BRG}
{Emerald}
Cyan
Orange
Fruit
Orange
Apple
(I actually had a couple of other trees, but this is enough to demonstrate how they actually work.)
And it turns out synonyms don't work quite like I expected them to, and are, honestly, so limited I question their value.
Test1: Tag a photo with the keyword Cyan. Only Cyan gets applied to the metadata, not any of the words associated with it (Blue, Colors, Azure). Searching, I can find the image by searching on Cyan, or Colors. But NOT by searching on Blue.
Test2: Tag a photo with the keyword Blue. Only Blue gets applied to the metadata, not Cyan, or Azure. When searching, I can find it by searching on Blue, or any of it's synonyms (Cyan, Azure), or Colors.
Test3: Tag one photo with Cyan, and another with Blue. Searching with Cyan gets me both images, as does searching with Colors. Searching on Blue gets me only the image tagged with Blue.
Test 4: Tag a photo with the word Colors (and nothing else). I find it by searching ONLY on colors, not Blue, Cyan, or Azure.
Test 5: Tag a photo with the word Red (and nothing else). I find it by searching on Red, or Colors, but not Pink or Rose.
Test 6: Tag a photo with the word Pink (and nothing else). I find it by searching on Pink, Red or Colors.
Test 7: Tag one photo with Orange->Color, and a second image with Orange->Fruit (this nomenclature seems backwards to me, btw. It's really Fruit-Orange and Color-Orange, but whatever...) Searching on Orange finds both images. Searching on Color finds only one, searching on Fruit finds only the other.
I had expected synonyms to work the other way, I think. So that if I searched on Blue I'd get all images tagged with Blue, but also those tagged with Azure and Cyan.
So kikashi is partially correct. Synonyms do affect only search, and not tagging (assignment). Searching on a term that is a synonym will find images tagged with the main word. (e.g., search on Azure and you'll find Blue).
But the statement that you'll find "any image which bears that keyword or any keyword BELOW it in the hierarchy" is backwards. You'll actually find images using the keyword, it's alias, or any word ABOVE it in the hierarchy. So if an image is tagged with Red, you can find it by searching on Red or Colors, but not Pink. If the image is tagged with pink, you can find it with Colors, Red or Pink, but not Salmon.
The worst limitation of using synonyms is that when you're tagging an image, LR3 isn't smart enough to know the synonyms exist. So if I tag an image with the word Azure, LR3 doesn't substitute Blue, or use the synonym where it already exists in the hierarchy.
It creates a new, top level entry named Azure.
It does seem like it would be useful to be able to enter Red as a search term and find Pink and Rose, too. The way it's implemented now forces you to enter the term you're most likely to use (Blue, for example) at the bottom of the hierarchy, and the least used words above. Or to use synonyms, and hope you never get confused an enter a synonym as a keyword instead of the word it refers to.
It seems to me it's more useful to just use Azure as another keyword beneath Blue in the hierarchy. At least that way if I tag an image with Azure, I'm not creating a new entry in the Keyword list. I'm not sure I see much value in synonyms as they're currently implemented, but if someone has some examples of how synonyms benefit them I'd be delighted to see them.