First, if the time button really did take them back to the start of the series,does that mean it could be considered canon in some way, that Comedy Central aired 'Space Pilot 3000' after the finale? This raises the question that, if looked too deeply into, everything could have changed if there wasn't a stable time loop progressing Fry to getting cryogenically frozen, thus effectively creating more time-streams that branch from the original, including one where everything is the same as originally intended, one where Fry never got cryogenically frozen, and possibly another that I'll go into right now.
Secondly, another time-stream could theoretically 'break down' due to a flux in it's rule of only going 'one way'. In 'The Late Phillip J Fry', we see the universe continually end and begin again, until mostly everything is the same. This obviously isn't an occurence that could naturally be replicated. But through this new timestream that goes only one way, this could alternatively cause it to break fown as the stream tries to 'replicate' the original, only to end when the universe itself does through having to ignore this time-travel.
An alternate theory of 'The Late Phillip J Fry', is that the time button somehow negated the 'end of the universe' concept of this episode, but there isn't much to go on with this theory.
The last theory ties with the first, and does make Futurama as a whole a lot more sombre or sad. This theory is that, had the time button really sent them to the time of 'Space Pilot 3000', and before Fry was cryogenically frozen, one timestream would be either much better or worse than the true 'original'. This timestream would involve Fry never being frozen, either because Nibbler failed to do his job of making sure this happens, or Fry himself prevents it. Maybe he read the note early and realized the delivery that night was a prank, so he went home or whatever. Maybe there was some kind of accident or maybe he just plain quit his job, but whatever happened this timestream allows Fry to continue living in the past.
One last theory that stems on this is quite sad, yet also hopeful. This theory suggests that, if Fry had gone back to 'Space Pilot 3000', he had no choice but to get cryogenically frozen, obviously because of Nibbler. This would mean that Futurama remains on a somewhat stable time loop, and Fry and Leela really can 'go around again', as long as everything happens almost exactly the it also means that Fry is destined to never see his family or Seymour again, becaise he'll always have to get frozen.
So these are my theories about Meanwhile, and are in no way canon. I may have more theories I can tell you about later, but right now I must sign out. So until next time, Goodbye!