Some will disagree with this...but here goes.
There always seemed to be a lot of tension in Jan & Dean's relationship due to Jan's role as producer of the music. To be fair to Jan, the results of his work are still here for all of us to hear in Jan & Dean's timeless recordings. With regard to studio recordings, he seemed (to me) to regard Dean Torrence's voice as another musical instrument. It appeared that Jan was always willing to find another vocalist to sing Dean's parts if Dean was not available to come to the studio at whatever hour that Jan was recording.
On "Folk & Roll", it seemed (to my ears) that Jan accomplished the album with very limited participation by Dean. It sounded like most of Side 1 (other than "Hang On Sloopy" ) was recorded with assistance from P.F. Sloan and Steve Barri (a/k/a "The Fantastic Baggies"). Dean recorded the solo vocal on "Yesterday" and performed with Jan on "Turn Turn Turn". The latter song confimed to me that Jan & Dean still harmonized very well. However, it may have been during the recording of "A Beginning From An End" that Jan threw Dean out of the studio after Dean's complaints about the song. It also appears that Dean was not a fan of "The Universal Coward" and, perhaps, did not want his name on the record.
As a result, two songs from Folk & Roll ("I Can't Wait To Love You" and "The Universal Coward") were released as a Jan Berry solo recording.
This would seem to imply that a split was imminent.
However...
The follow-on project, "Jan & Dean Meet Batman" featured heavy involvement from Dean. Throughout their career, it seemed (to me) that Dean played a greater role in Jan & Dean's comedic persona than he did in their recording career. The "Batman" album gave Dean a chance to shine, and perhaps the hours he and Jan spent on this album healed some of the rift that may have existed between them. The next album, "Filet of Soul", featured more comedy and also seemed to be more of a collaboration between Jan & Dean.
There is no way of knowing whether "On the Run" would have been picked up by ABC. While the pilot that many of us have seen on youTube features the typical Jan & Dean humor, the dialogue seems a little tentative. I am not convinced that ABC would have taken this show seriously except as a summer replacement show. However, William Asher (who produced his wife, Elizabeth Montgomery, in Bewitched on ABC) may have been able to exert some influence to get the show on the air, and Dick Clark might have even put in a good word for his friends Jan & Dean.
So, assuming that On The Run was accepted for at least a short run, it would have afforded Jan & Dean a new platform for promoting their music. One could reasonably assume that a soundtrack album would have been issued in the wake of the show, featuring some of the silly songs like "Time And Space" as well as a few "serious" Jan & Dean songs that Jan would have produced. Dean would have no doubt been a participant especially if the songs were used in the show.
At the same time, Jan would have been continuing his studio experiments with "Norwegian Wood" and "Louisiana Man" along with some of the tracks that are now part of "Carousel of Sound". Liberty Records, who initially resisted "Norwegian Wood", might have changed their mind if the song had received exposure on the TV show and recieved a favorable public response. This would have given Jan an improved bargaining position with Liberty or another prospective label. Perhaps that would have opened the door for Jan to produce other artists.
The increased exposure that resulted from a TV show would have no doubt led to more touring opportunities for Jan & Dean. This would have, most likely, extended their career for a couple of years. Dean would have played a prominent role in the comedic part of the stage shows, and the talk of a split between the two would have died down.
The true test would have been whether Jan's continued musical vision would have remained commercially viable. For a while, at least, the TV show might have assured a favorable audience for Jan & Dean's recordings. However, we will never know how Jan might have responded musically to The Summer of Love and Woodstock. Carnival of Sound would have no doubt evolved from what we ultimately heard. Would Dean have suggested any of the songs he recorded for Save For A Rainy Day? Would Jan have listened to Dean's suggestions or ignored them? A combination of the two albums might have been a viable release.
As the sixties wrapped up, the first signs of a rock and roll revival would have emerged. If Jan & Dean's Top 40 career had started to stall by this point, Dean might have suggested embracing the nostalgia phase as a sound business move. Jan, on the other hand, might have rejected such a move, preferring to focus his efforts on producing other artists and releasing singles as a solo artist.
And all of this might have been academic had Jan been inducted into the Army. The TV shows and the tours would have been shelved, and Jan might have had to rely on Dean to keep things going. (But that is another parallel path through history...)
I guess the truth is we will never know how things would have been different had Jan not been severely injured in April 1966.