Most know the Paul is dead urban legend in varying levels of detail. The story goes something to the effect that in 1966 Paul McCartney, distraught over a recording session, stormed out of the studio and drove off, or that he was driving a girl home (Lovely Rita). Along the way, he got into a car accident ("He blew his mind out in a car,"; "I took her home, I nearly made it"), and was decapitated ("You were in a car crash, and you lost your hair"). The Beatles and their managers paid off the police to cover up the death, took the winner of a look alike contest (usually named Billy Shears, William Campbell, or William Shears Campbell), but were so distraught that they hid clues throughout their songs and in album art, and so forth. This would also explain the gap between recorded material during that time, and the revolutionary direction the band would take.
But what if Paul McCartney actually did die in a car crash in 1966? What would the Beatles actually do, and what would actually occur?
When in 1966? Assuming November 9th 1966 per rules of the urban legend I think Strawberry Fields Forever was already written, so that song would likely still be recorded at some point. Though I would imagine Lennon taking McCartney's death pretty hard, especially when we consider its an automobile accident, and therefore might resurrect memories of his mother's death all those years back. He could either react belligerently or quiet mournfully as he had when Sutcliffe and Epstein died historically. If we're lucky, Lennon doesn't want to deal with McCartney's death, so he gets to work to try to distract himself. Meanwhile, the reaction to McCartney's death will be hysterical. You'll hear an awful lot of talk about it being the end of the Beatles, and you'd likely get a contingent of fans with exactly that attitude, ie nothing after McCartney counts as being by the Beatles. There is a chance that the group would split up, but somehow I think they'd at least make an attempt to keep things together, however temporarily. Also, Lennon wrote some very good songs in late 1966-1967, but he was extraordinarily lazy during the time period, that's one of the reasons Paul ended up sort of taking over the group, so that puts a monkey wrench in things. I also think Revolver, being the last album featuring McCartney, probably goes back into the charts. a Yesterday single is re-released. I could imagine Lennon writing a song quiet similar to a Day in the Life about McCartney's death. A few songs might be recorded quickly, but I'd imagine a full album would take an awfully long period of time to put together. I don't think they'd spend much time recruiting a new member, I think the band probably gives bass duties to Klaus Voreman. Its debatable whether or not he actually gets to officially join the group or not
I know you want to know what happens if the death occurs in 1966, but in my opinion, if you want a McCartney death in a car related accident, there two time periods I can think of for an actual event that could be manipulated to produce that kind of result, neither of which happens to be in 1966. If I remember correctly, Paul
was involved in a motorcycle accident in late 1965, it left him with a chipped tooth and a scarred lip. It might be a simple, if morbid matter to turn that into a fatal accident. If I remember correctly said accident occurred on December 26th 1965, less than a month after the release of Rubber Soul. If you think a reaction in late 1966 would get you hysteria imagine it happening a year earlier. (By late 66 the bands popularity was beginning to lessen. While Pepper did restore the groups popularity, such a restoration was not really expected at that time.)
The other event is based on something I've read, and it may be equally untrue as the whole death hoax itself. The event is not as well sourced as the motorcycle crash. Essentially, someone did crash Paul's car pretty badly on January 7th 1967 but Paul wasn't in the car at the time. So you could put McCartney in that car, and have a potentially fatal accident.
If the event occurs in January of 1967, the band has already been recording for a while, and you likely have about four songs more or less completed (or, at least takes which could reasonably be made into releasable material.) Strawberry Fields Forever, Penny Lane, When I'm 64, and Harrison's Only a Northern Song. That kind of situation makes the completion of an album, however long it ends up taking, a much easier endeavor than a late 1966 death would