The consequences would be
The war is winnable for Lizzie.
Would be good that will review the history of the period from a neutral source...and given that the Habsburg Empire was the dominant military power in Europe during that period... since human conflicts with all its variables are unpredictable and definitely (for more than your cultural formation, perhaps so it does seem) are not a boxing match or a game of football where a team is the clear favorite or have winnable games before playing.
an Anglo-Dutch state would be interesting but I wonder what France would do, given their relationship with England and interest in the Low Countries.
Apart from the seriousness and support the offer and the very good reasons for its rejection ...
The consequences would be that Spain, fighting would follow and would not accept even a truce or the union of the two nations, whose ally to France, although enemy of the Habsburgs would look like an immediate and deadly threat the union of England Netherlands (United Provinces) in one nation. If their economic and commercial rivalries, allow them to join or remain united.
Religious differences between Anglicanism (mixture of Catholicism and Protestantism under the authority of the monarch) and the predominant Calvinism in the Netherlands, not to mention its religious tolerance for non-Catholics course.
The English monarch on the other hand was not very tolerant of religious dissidents opposed to the organizational structure of the Church and its role within the Church of England.
The new nation should face a total war on the continent, which should devote all its resources for decades; because most likely Habsburg, is what they would do, because before this union happen, they saw a Rebellion partly funded with the support of England, now will see the union of the 'rebels' Dutch and English under one monarch as a direct threat to their possessions.