The movie is beloved because of it's stars but the basic story is so strong I get the feeling it would have worked with a bunch of other people in the role - Greer Garson, say, or Errol Flynn.
It's a very good script. The concept is so simple and strong its surprising it took so long for this to get made... a mismatched couple travel downstream together in a boat to blow up a German cruiser. The structure is highly effective: introduce Rose, introduce Charlie, awkward dinner and news of war, the Germans attack, Charlie returns and takes Rose, she gets the idea of what to do, he goes along with it but then gets drunk (paying off the essential conflict between the two characters sooner rather than later), she pours out his gin and gives him the silent treatment until he relents, they go down rapids and pass by a German fort, have sex, get stuck in the mud.
It's all logical and well thought out. There are two deux ex machinas towards the end - they get out of mud by a convenient rain (after Rose prays) and the boat at the end being sunk by the wreck of the Queen. But it's a marvellous ending with the two of them getting married. Great fun and one of the best star vehicles of all time.
(I should add though the film features a lot of non-very-casual racism of the period. The non white African inhabitants are completely depersonalised, referred to as "blacks", "natives" and that's about it.)