Hey, so nice to see you again! 
Let me try this once...
First I imagine, Vichitra ji had 0 actual power in HP, given administration of the country, post Shantanu and until Pandu, had always remained in Bheeshma's hands. Also, given the guy was not even interested enough to go pick up his own wives (I mean let Bheeshma fight, but at least he could've given them a ride!) I do not feel he would've given much importance to Amba's complaints anyway.
As to what if they had gotten married, if we go with BA's version where they just get a legal sign-off but continue to live separately, then I don't think MB would be changed much...only there'd be a lot more gossip about dear old Pitamaha! 
Now the case if they got married, and actually fell in love. Even in this case, if they had a girl, nothing major would change (unless the kid turned out trans...I'd pay to read that!). Either Satyavati would still bring in Vyasa and the 3bros would be born, or the daughter's kid would be adopted into the family, like Chitrangada and Babhruvahana.
In case Bheeshma and Amba had even one boy, that would drastically alter the line of succession. I mean, given Satyavati talked Bheeshma's head off about marrying every time they were at this crossroad, I'd think she would be jumping for joy and would personally crown the kid or whatever.
Now, ideally in this case Vyasa would not come into the picture at all, and none of the next drama would happen at all. But for the sake of making it spicy, lets consider maybe Satyavati got paranoid (can't really blame her) about having just 1-2 kids from Bheeshma, and the 3bros were born anyway.
For some time, I guess, it would have progressed the same way as it did. Dhritu would still be blind, so Bheeshma would get him Gandhari, and with her would come Shakuni. Kunti would still choose Pandu (as I personally believe she came to HP because she knew where Karna was and wanted to be close), and Vidur is well...Vidur. That man is untouchable!
Now, 3rd gen would complicate things. Here if Bheeshma's kid became Bheeshma part 2 and didn't have kids, then toh again, same as it is. If they have kids, then it would depend on the birth order. Simplest resolution: this kid is oldest, Yudi is relieved to be the spare not the heir and probably just becomes an ascetic somewhere, and Shakuni doesn't get the 'in' to start poisoning Dury because Dhritu is also not the king. Honestly, probably 5Ps wouldn't even be born, given Pandu's issues, if there was already an heir, Kunti probably wouldn't bother with her boon.
Now, I believe, since Amba and Bheeshma are both pretty stand-up people, their 100% involved upbringing would surely have some positive impacts on their kid(s) and grandkid(s), so if there is a conflict, they would most probably side with the Pandavas. Although, if Bheeshma had his own kid, he would probably be more proactive about protecting the kid by paying proper attention to both Dury and Bheema's escalating conflicts and nip it in the bud. And probably, they would think about the kingdom divide a lot sooner, and three ways instead of two.
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