Does the entire party agree to leave with Narracott in the morning in And Then There Were None ?

No, only seven of the ten people invited to the island are on the boat with Fred Narracott.  He observes that they are a mixed and unusual group of people.  The seven on the boat with him are:Mr. Justice Wargrave;  “an old maid” who would be Emily Brent; “an old military gentleman” who would be General Macarthur; a “nice-looking young lady” who would be Vera Claythorne; a “bluff, cheery gent – he really wasn’t a gentleman” who would be Mr. Blore; a “lean, hungry looking gentleman with the quick eyes” who would be Captain Philip Lombard; and finally, “the one who had arrived in the car” who would be Tony Marston (all quotes are on page 23).

Two other people brought to the island are Mr. and Mrs. Rogers.  They are the butler and the maid and have already arrived and prepared the home for Mr. and Mrs. Owens and their guests.  They have not met the Owens and have just arrived on the island.

The last person is Dr. Armstrong, who arrived just at sunset.

 “Dr. Armstrong came to Soldier Island just as the sun was sinking into the sea” (pg 29).

He was the final guest.  So, seven came on the boat, two were already on the island, and one came at sunset.