I have to say it seems like it was actual, genuine Elvish ancestry rather than a sort of 'Elvish air' such as Frodo had, simply because 'elven-blood in his veins' is fairly specific.  I'm trying to dredge up some memories of Legolas bowing to anyone other than Imrahil, and if so were they elven or human?  Sadly I don't have the book with me, so I can't check it.  But I would definitely suspect it was real Elven heritage.  How, I don't know! 

Legolas is indeed being rather tactful!  Not just a pretty face, despite what the Orli-fans may say.  I imagine that as an Elf, he would have the experience to realise how important a smooth transition was.  He had probably seen (or heard tell of, at least) many political bunglings, and wanted to avoid the worst--partly because Aragorn was his friend, and partly because Gondor was the last free kingdom of Middle-Earth, on which all their hopes rested!

Is it just me, or is it a little amusing that he doesn't refer to Gimli by name, but just as 'this Dwarf, my friend'?  Perhaps he was trying to give the poor dwarf a little credibility in Imrahil's eyes, seeing as, if he were part Elven, he might not look too kindly upon dwarves.
Of course, it's also possible Legolas pointed him out so Gimli wouldn't feel compelled to introduce himself, and say something untactful about hewing.  Or, if it comes to that, Imrahil might have mistaken Gimli for a very hairy horse and have been about to remove him from the City, seeing as animals weren't allowed in certain parts.

It is significant that Legolas did not presetn himself in 'official capacity'. It was definitely not the Elves' war. he was helping out, but he could not promise the aid of his kinsfolk in battle.  He had no right to.  And perhaps he felt it would be unfair to give the Men false hope by proclaiming himself as the Prince.  After all, look at the cufuffle that ensued when everyone thought Pippin had come to bring aid!  So, very wisely, Legolas just presented his own sweet self.

BOROMIR:  One day our paths will lead us there, and the Tower guard will take up the call--the Lords of Gondor have returned!
ARAGORN:  Dream on, mate.  You'll be in the back row cleaning my shoes--did I just say that out loud?