My answer is no. Because:
1) Misty and Ash already have a history as travelling friends that would become awkward in such a situation.
2) Rivals compete for the same goal. Misty isn't competing for the same goal as Ash, as she is a water type trainer and doesn't participate in leagues.
3) The battles Ash and Misty have had were in my opinion dissapointing as the writers seemed to go out of their way not to make one win properly against the other. (Either by cutting the battle short or using Psyduck.)
4) Misty is a Gym Leader and Ash regularly defeats Gym Leaders, even the very strong ones.
5) Part of the fun of a rival is discovering their personality and backstory. Misty already has this stuff so the rivalry wouldn't be as interesting.
6) Misty is a gym leader from Kanto. What would she be doing in Isshu/other region? And if she was travelling there, wouldn't she want to join Ash?
So, yeah, no.
I agree with this.
And Misty only trains water types. Rivals train more than one Pokemon type.