Actually, if you take that appearance on Dick Cavett's show as consistent with one of the sub-themes of the film...that Gump was responsible for a number of historical and cultural happenings throughout the 60's and 70's (Watergate, the running craze, the happy face t-shirt) then that reference to 'Imagine' makes no sense.
The reason?
'Imagine' was released in 1971. Gump's appearance on Cavett's show was in 1972.
Watch the film again. You'll see.
Now Sam!
Next thing I know, you’ll be trying to tell me that Lt. Dan COULD NOT have invested Gump’s money in some fruit company.
“Lieutenant Dan got me invested in some kind of fruit company. So then I got a call from him, saying we don’t have to worry about money no more. And I said, that’s good!”