TLDR: Probably not. For most F2P or newer players, it's hard to justify pulling Pollux without either A) investing heavily into a banner right before a major half anni update, and notably a half anni character in GMurphy, and B) when Castor and Tawil, two of arguably the strongest characters in the game, are also running. At low investment, Pollux is effectively a "premium Jenkin", doing more personal damage at the cost of more setup time. For most players, I'd recommend securing Castor and Tawil at bare minimum first, then considering their dupes, and THEN consider pulling Pollux (with the idea of either getting or working towards eventual OE). With that said, Pollux is fine despite the community backlash, but for most players, Jenkin exists (who is already the gold standard for both Ultra DPS AND F2P DPS).
This took me over a week, with multiple revisions, before I felt satisfied shipping this out. With that said, here's a significantly more paired down write up for Pollux.
Pollux is a strange character in gameplay, abandoning Leap effect entirely in favor of just activating his own version of it on his first card used each turn. Combined with his Sacred Heart card that he creates and "juggles" into his deck on use, and you have a fairly unique Ultra character. However, Pollux is a VERY expensive character to utilize. At E0, he relies on a well invested Castor as his own personal damage is generally too slow compared to other limited DPS. Without Castor, you'll want at least E3, and ideally OE, to deal the huge damage output that he absolutely can do despite the community memes.
Pollux's damage primarily comes from his passive [Atonement by Pain] that adds 200% ATK bonus damage to his first played Command Card. This represents a substantial boost in his damage output, especially when combined with his Bleed stacking. However, it does take time for his damage to scale up at low investment; with dupes, you can speed this up drastically, but needing dupes to even function properly as a main DPS is a terrible place to be (hi Kathigu-Ra).
Many originally assumed he would be Castor's best teammate. This has not proven to be the case. While Pollux certainly appreciates what Castor provides, and can even draw Feathers from the deck with his 2 cost, Castor pairs far better with Jenkin, who has an easier time proccing Castor's Corruption and even buffs Castor's Crit DMG. With that said, Pollux certainly scales much higher due to both being a limited and being an arc 2 character, so from a personal damage perspective Pollux wins out.
With enough dupes, Pollux can unshackle himself from being just a Castor sub DPS and becoming a full fledged destroyer in his own right. His OE represents a massive increase on his nuke turn, giving him 50% of his [Atonement by Pain] for all his Command Cards for the rest of the turn. This can lead to not only an absurd amount of damage, but also an absurd amount of Bleed stacks. Of course, the opportunity cost in pulling or shop duping him to OE compared to other characters is something that you'll have to decide on.
Ultimately, I think Pollux is a good, if flawed, character. He does a lot more than most people seem to feel comfortable admitting, but the amount of investment needed is difficult to justify. With a highly anticipated half anniversary character coming out very soon, as well as highly anticipated reruns for both Castor and Tawil ongoing through his release banner, I struggle to see why someone would drop pulls into this banner from a meta perspective. And with every limited DPS at OE being able to deal insane damage in arc 2, I doubt there won't be another "insane at OE DPS" released soon after that'll be the next best "insane at OE DPS".
But hey, Morimens is a pretty open game. Anything can work if you funnel hard enough.
