Answer: The Gemara (Avoda Zara 75b) writes that any kelim used while eating require tevila. The Shulchan Aruch (YD 120:4) extends this to kelim that are used in cooking or food preparation such as barbecue grills.
Nonetheless, the Rema (YD 120:5) writes that while one doesn’t use a chalaf, knife for shechting, for preparing food, one should ideally tovel it without a beracha. The Shach (YD 120:10) explains that this is because it can be used for other food purposes.
R’ Asher Weiss (Minchas Asher 3:62) writes that a kos shel Eliyahu fits into a similar category as it may be used for drinking. Additionally, one may come to use it years later for kiddush, especially if one finds another, nicer kos for seder night. Thus, it should be tovelled without a beracha (See Rivevos Ephraim 1:122).
In the following teshuva (ibid. 3:63), R’ Weiss writes that there is no need to tovel a seder plate, however, as it is not used for eating off or for preparing food. While some make a point of eating the food from the seder plate, it still serves as a tray for displaying the symbolic foods.
In conclusion, there is no need to tovel the seder plate, but one should tovel the kos shel Eliyahu without a beracha.