Probably hte opposite, it would strenghten the position of Frederick Henry, but this coudl change after his death.
I doubt it. Yes it would be a great victory, but not so big that it would increase the power of a stadholder, who was already known for conquering cities.
Most important is that there will be a major city outside the state of Holland. Even if Antwerp is at that time a shadow of it former glory, the patriciens of the city would do anything to gain influence, poewer, presitge and whealth whitin the Dutch Republic. It could counter balance with coalition cities the power of Amsterdam.
Antwerp would be in an interesting postion. Personaly I would say that at first nothing would change. Antwerp will be a catholic city in a "province" that isn't a province. Since its fall, Amsterdam will remain the most important city and the city of trade. So at first I believe the political situation will remain roughly the same in the Dutch Republic.
This will change though. Antwerp is a perfect port. Some enterprising merchants will take advantage of it and they will become rich and influential. Antwerp will take advantage of it and will become richer, but it would still lack any influence. At one point this will lead to pressure to change the current situation in the Netherlands. Merchant in Antwerp will demand more influence, probably supported by people opposing the power of Holland (like the prince of Orange). I expect that Antwerp will see an increase of protestantism, partly from people moving towards Antwerp from Holland and Zeeland and partly from new converts who want to move up in life. This will make it easier for people to accept Antwerp as equals.
At some point Antwerp (and probably all of Brabant) will be excepted as a full Dutch province, or at least it will be given the status of Drenthe (self governing, but no seat in the estate general). Since Antwerp is so close at the border and will be an important and rich city, I assume they want it better protected against foreign invaders (France). So they may extend the waterline towards Antwerp (Napoleon wanted that too). They probably want to conquer part of the hinterland to have a larger buffer, which means that a larger part of Antwerp and Flanders becomes part of the Dutch republic. Of towns like Ostend, Bruges or Ghent are part of it (relatively likely) that would mean that some major Flemish towns become part of the Dutch republic, possibly increasing the influence of Flanders.
A Dutch Antwerp would certainly change the political landscape of the republic, although it would probably take a couple of decades to see the result. Somewhere around the the early 18th century would be my guess.