No, they couldn't, because the airlock of Icarus I had been severely damaged; once they broke the seal of the outer door (when they got out of Icarus I), it couldn't be closed again and be repressurized. Your idea was explicitly dismissed when Harvey suggested that he (and not Capa) should take the one space suit, and that he would go back to Icarus II and do "everything in his power" to save the others: it couldn't be done.
From http://www.subzin.com/search.php?title=Sunshine&title_id=M239356899&search_sort=Popularity&type=All&pag=33:
Searle: What happened?
Mace: Airlock's destroyed. There's only one suit. Capa's taking it.
Searle: Why Capa?
Mace: The rest of us are lower priority.
Harvey: I'm not a low priority.
Mace: You're a comms officer on a ship that has no communication.
Harvey: I am the captain. The mission needs a captain to hold it together.
Mace: Harvey, Capa's the only person outside of Icarus who can operate the payload. There is no choice.
Harvey: No, there's no choice for you. Capa, I order you to remove that suit. Get out of the suit. That is a direct order. I assure you, when I'm onboard Icarus II that I'll do everything within my power--
Mace: To what? Shuttle back with more suits? The airlock is ripped in half. Once we break that seal, how are we gonna re-pressurize?
(I may have the characters of the first four lines incorrect; but that doesn't affect the point of the discussion between Harvey and Mace.)
Furthermore, since the computer was down, the airlock seal could only be operated manually from inside Icarus I (behind the inner door), that's why Searle had to stay behind. And Searle didn't mind, he was thrilled at the prospect of getting to the observation deck of Icarus I and experience the Sun from up close with his own eyes.
Narrative-wise, Searle, like any of the other team members, had to die because he had made a mistake earlier and hence had to redeem himself by sacrificing his life for the greater good.
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