Presumably not; it does not seem the type of item that would be left behind. I think it possible that Fëanor made sure all of the palantíri in Tirion came with him to Formenos when he was banished.
We are obviously playing a game here. We don't want there to be any palantíri in Middle Earth during the First Age. If there were, it would complicate the story and make some people's actions seem...idiotic. The Noldor can't have any, and Morgoth certainly can't have any (or else the Hidden City of Gondolin staying hidden for 400 years seems a bit...much). So, we won't have any; no problem. But then the question is raised...if Fëanor made the palantíri (and Gandalf seemed to think he did), then why weren't there any in Middle Earth during the First Age? Why didn't the exiled Noldor bring some with them from Valinor? The story-external reason is that Tolkien invented the palantíri while writing the Lord of the Rings, so of course there were no palantíri when he first wrote the stories of the First Age. But we need a story-internal reason to explain their absence (and then later presence in Numenor).
There were two choices. Either we could make the palantíri a later invention, not the work of Fëanor at all...or we could find a way to make sure no palantíri were in Noldor hands during the rebellion, and thus none made it to Middle-earth. We chose the latter. Fëanor might think he can make more after his arrival, but his early death puts a stop to that possibility. (Or maybe some component required to make them is only available in Valinor.)
So, in Silm Film, Fëanor makes the palantíri mid-way through Season 2 (same episode where Melkor is released). This is before he makes the silmarils, so it's his greatest craft project to that point. Then, he shows his father Finwë what they can do - it is meant to be a gift so that Finwë can look back to Middle-earth for his friend Elwë. Finwë does not see Elwë in the palantir, but he does praise Fëanor's cleverness. Finwë decides to give more palantíri to the Teleri as a gift, because he thinks surely they will want to look back to see their relatives they left behind. The Teleri also find them useful for ship-to-ship communication, so they prize these creations of Fëanor's. Fëanor himself moves on to bigger and better things (the silmarils) and no longer shows much interest in the palantíri. Then, when Fëanor is banished from Tírion, he moves his entire household to Formenos. Any and all palantíri come with him. When Morgoth attacks Formenos and kills Finwë, he smashes all of the palantíri and steals the silmarils. IF Morgoth takes any palantíri from Formenos, they are all eaten by Ungoliant before reaching Middle-earth.
So, the last unaccounted-for palantir was one we decided was present on one of the stolen Teleri ships. Amrod pockets it (in Season 3 Episode 2) and keeps its existence secret, and it is lost in the Shipburning. Thus, the appearance of a palantir in Season 3 Episode 8 will be the last time we see one until the elves of Tol Eressëa gift some to the Numenoreans. That gap of time will make the uncertainty feel real (are these the same ones Fëanor made, or are they the work of a later craftsman replicating his achievement?)