In HoME there is an essay on the laws and customs of the Eldar regarding marriage which includes some information on elvish procreation. So rather less than anything is possible if this is taken in to account. Also I think it is vital to remember that Elves are immortal and so aren't driven by the same biological imperative as mortals.
Firstly Elves cannot remarry (Finwe was the disastrous exception that proves the rule). Because an Elvish death within Arda is temporary it does not end the marriage. Pre-marital sex is not possible for elves and extra-marital sex is not an option either so no half sibs. If you want to know why read Morgoth's Ring or
this highly informative and amusing article.
Now as is explained in LACE having children is more permanently debilitating for elves than humans and families with more than 3 children were uncommon.
Feanor was unequalled as the father of seven sons. Now this was in Valinor when the Eldar were at the height of their vigour and Feanor is almost certainly the most vigourous Elda ever (remember Miriel saying he had taken from her the strength of several sons).... not a huge surprise that Nerdanel chose to stay behind. The other recorded larger families (of Feanor's brothers) are all Valinorean born. Although elves don't die in Arda their spirits start to dominate over their bodies and their immortality seems more burdensome. Physically and emotionally it is unlikely that there were many if any very young elves at the end of the third age. Arwen was not known as the Evenstar for nothing. At 3000 she was quite possible the youngest of the Noldor - certainly of any significance. Celebrian's ability to make a full recovery in Middle Earth may have been compromised by having born 3 children late.
While it is probable that the Sindarin and silvan elves who were staying in middle Earth may have been less effected by fin d'epoque ennui, if Legolas had siblings (finally getting to the point) he was unlikely to have had more than 2. Certainly the fact that they aren't mentioned is not decisive. Fond as many of us are of him, Legolas was the last to join the Fellowship (in terms of book development) and though he has my favourite speech in the whole book and provides a few insights (he also has a few regrettable "tralalally" moments) into the elvish mindset we know least about his background than the rest.
As for Thranduil taking a chance by sending his presumably only son to Rivendell - well he surely would have had companions on the journey- and it was a "high level" conference. Thranduil wouldn't have sent just anyone and for the story it was symbolically important that it was someone of high status in their own community. If you look at the dwarves family tree, Gloin and Gimli are the closest living relatives of Dain and his heir. It is appropriate that someone of similar status is witness to the handover to the age of men.
So after all that the answer is maybe but since they weren't relevant to the plot we don't know. However when I RPGed Thranduil elsewhere I gave Legolas a younger sister .... but I am not claiming that as canon...
