No, There shouldn't be anything that affects your playthrough for changing jobs while doing the MSQ. My friend leveled up well over 5-6 jobs while on his journey to finish the MSQ. It's always recommended to try out new jobs on your first playthrough!

Do you still have road to 70? All jobs under 70 should have the buff during that time even if you change jobs. All jobs that are lower level than your highest level job have a 100% boost so you don't really need to make a new character on a different server just for road to 70.

If you don't have it then it depends on you, if you think its worth making a new character for.