If they will be facing the Sixers, not having Giannis will be an easy lose for them that's for sure especially now that Embiid's back already. If they will be facing the Heat "AGAIN" in the first round, well we know what happened last year. I'm not saying that it will happen again this year, but who knows. That would be the most embarrassing moment for the Bucks, and knowing that they have Doc "CHOKE" Rivers as their head coach, we might see Giannis leaving the team in the off-season. 
I doubt Giannis can leave the Bucks in the offseason, even if the Bucks screw up in the playoffs. It's worth noting that Giannis has a huge contract until the end of the 26-27th season and a player option for the 27-28th season. Not every team will be able to take a player with such a huge contract, and the Bucks won't just give him away. Besides, this is only the first season when Giannis and Dame perform together. I think if they don't win at least one title, both of them will leave the team after 2-3 seasons.
Not every team can afford his contract but there are some that would damn sure make some moves to accommodate him and his contract. The knicks, Boston, and who knows who else might be interested. Giannis is a commodity that every team would explore if he becomes available.
That's what I'm also thinking.
For sure those teams with huge salary cap space will try everything just to get Giannis just in case he demands a trade if they will not be a competitive team this playoff.
Knicks can be one since they still have a huge cap space. As for the Celtics, with the re-signing of Porzingis and Holiday, I don't think that they will be interested in getting Giannis still and for me, that would cause a huge imbalance in the East that it might affect the competition. The Jazz can be a candidate as well, but I guess let's see how they will perform in this year's playoffs and after that, we will see how Giannis will react on it.
My prediction on them is that they will at most reach the Conference Finals but will be beaten by Boston. The bad thing though is that they might face either the Sixers or the Heat in the first round, and they can beat the Bucks if all of them are healthy (at least for me).