No, look, he didn't have business when he arranged the trip. Cote even checked with his secretary. At that point, NOBODY knew about the trip except Mr Cote and Ms Needy. Cote found out about it by snooping.
Cote sat on her knowledge of this secret, until the secretary rang her - as is usual with his short-notice trips - to tell her he was going. Therefore, he only told his office about it several days AFTER he'd booked his flight in secret. He then fixed it with the office, who rang Cote.
As far as he was concerned, he'd arranged the meeting in secret. The he lied to his office. The lie to his office ensured the office would lie to Cote.
If she hadn't found it by snooping, she'd still be none the wiser.
But. When his secretary rings Cote, s/he ususally gives Cote both the flight details and the hotel details. This time, she only gave the flight. What this implies is that Mr. Cote told the secretary which flight he was on (presumably to claim it back & cover his absence) instead of asking his office to arrange transport & accommodation.
One of Cote's worries was that Mr. Cote may have paid Ms. Needy's flight. This turns out not to be the case (probably), as she's headed to a family reunion anyway.
But THERE IS NO BUSINESS TRIP, though I should imagine he's frantically trying to arrange one in that city - he'll have to explain his absence, and travel expenses, to somebody at some point. When he gets a client to cover him, he's free of retrospective queries from work.
If I were Cote, I'd be fixing up to meet his secretary for a Weirdly Intense Chat. But I reckon Cote's on it, in whichever way works for her.
Grace Poirot, over and out.