This is an interesting question Cigars, so I did a bit of googling. And it seems that the practice of taking mail out to an ocean liner, even shortly after a ship had left, was a real practice in the early 20th century, not just something Hergé invented for plot convenience.
Here's a web page with a diagramatical illustration form 1920,
http://www.gjenvick.com/SteamshipArticles/1920-04-AerialMailAtSea.html showing how some mail planes actually dropped mail down onto the ship below, without even landing on the water. And the example shown is of a package being delivered to the White Star liner Adriatic just an hour-and-a-half after the ship had left New York.
Presumeably the system shown in The Broken Ear, of landing a seaplane near the ship and transfering the mail with one of the liner's small boats, was also used. (I'd probably find referenece to something similar if I google-searched for long enough!)
Also, here's a web link to an article about the French transatlantic liner ÃŽle de France,
http://www.greatoceanliners.net/iledefrance.htmlwhich includes this interesting fact:
Even though the ÃŽle de France could not claim to be the fastest vessel in the world, she had the quickest mail-system between Europe and America. On board, she carried a small mail-plane that could take off 200 miles from shore, making the French liner the fastest in one aspect. I think Jock's thinking must be correct that there was enough commercial importance in getting mail accross the Atlantic as quickly as possible, or getting mail to businessmen etc on board the ship, to make it worth combining mail planes with ocean liners in these various ways. There was also great competition between the liner companies, of course, regarding who could get their passengers across the Atlantic fastest, so this presumeably also applied to getting the mail across. If you could boast that mail could be sent out to a liner that was already a few hours out at sea, then sent ashore at the other end when the ship was still 200 miles from shore, then presumeably this extra speed of delivery made people use your mail service instead of some other liner company's.
At some point in the 1930s, the development of big flying boats that could fly right across the Atlantic (and, for a time, airships) must have surplanted the liner-mailplane combination as the fastest way to get mail across the ocean.
But maybe the liners continued to offer an alternative, cheaper mail service for less urgent items. (I'm just guessing on this last point, though.)