Playing on a sponsor's invite, Harrington carded a six-under-par 65, his lowest score of the year, to lie a shot off the lead shared by Haydn Porteous, Joost Luiten and Nicolas Colsaerts at the Regnum Carya Resort.
"The reason I'm here is because if you win one of these two events, it puts you right there for the Ryder Cup," the three-time major winner said. "It would kind of be in your hands if you got a good start like that.
"The last half dozen years I've been thinking it's really tough to make this team, especially when you're playing this mixed schedule here and over in the States.
"Now I might be resigned to the fact that it's more about playing the right amount of tournaments and still needing to play and get lucky to make it.
"It's tough when three or four of our top players eat up a lot of [the eight automatic] spots. It leaves very little room for everyone else."
Harrington would be a likely vice-captain to European skipper Thomas Bjorn in 2018 if he does not look like qualifying and added: "Thomas has been very polite in not coming to me and talking to me like a vice-captain.
"He's leading me to believe I'm still a player which is nice. In a few months' time maybe that will start changing."
Poulter missed last year's defeat at Hazeltine after spending four months out of action following foot surgery, but is on the verge of getting back into the world's top 50 after slipping to 207th in February.
"I didn't know how long it would take to try and get back in, but good golf always moves you back up the board," said Poulter, who thought he had lost his PGA Tour card in April before a mistake was noticed in the points structure used for players competing on major medical exemptions.
"I've had a few opportunities of being in the mix to close out and I haven't done that. I guess I just need to learn how to win again and as soon as I do, then we can move up properly."
Rose moved into contention for a second money list title with his victory in the WGC-HSBC Champions on Sunday, but remains more than a million points behind his fellow Englishman, with 985,000 points on offer to the winner in Antalya.