Yes, Olympic met a natural death, a victim of the Cunard-White Star merger as well as the factors Adam cited.
But quite a few White Star ships met more violent ends, principally as war victims. The following ships were lost by White Star (or Cunard White Star) from 1869 on:
Atlantic, wrecked at Terence Bay, Nova Scotia, 1 April 1873;
Naronic, went missing in the North Atlantic, February 1893;
Republic I, sank off Nantucket after collision with Lloyd Italiano's Florida, 24 January 1909;
Titanic, sank after striking iceberg off Newfoundland, 15 April 1912;
Oceanic II, wrecked on Foula Island, 8 September 1914;
Armenian, torpedoed off Cornwall, 29 June 1915;
Arabic I, torpedoed off Old Head of Kinsale, 19 August 1915;
Cymric, torpedoed 140 miles off Fastnet, 29 April 1916;
Britannic II, sank off Kea Island after striking mine, 21 November 1916;
Georgic I, sunk by Germant merchant raider 500 miles off Cape Race, 10 December 1916;
Russian, torpedoed 210 miles east of Malta, 14 December 1916;
Laurentic I, torpedoed off Lough Swilley, 25 January 1917;
Afric, torpedoed 12 miles off Eddystone, 21 February 1917;
Southland, torpedoed off Tory Island, 4 June 1917;
Delphic I, torpedoed 125 miles off Bishop Rock, 16 August 1917;
Celtic II, wrecked on Roches Point, 10 December 1928;
Laurentic II, torpedoed off Bloody Foreland, 3 November 1940.
In addition, while not technically a White Star ship, Justicia was under the line's management when she was torpedoed to death in July 1918, while Baltic I, Asiatic I, Gaelic I, Belgic I, Doric I, Cufic I, Runic I, Medic, Runic II, Suevic, Traffic II, Zealandic, Ceramic, Bardic and Pittsburgh were lost after passing from White Star to other owners.