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.
'Imagine' was released in 1971. Gump's appearance on Cavett's show was in 1972.
Watch the film again. You'll see.
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!”