Yes and no, and this answer is quite dependent on knowing the foreign policy preceding Wilhelm II’s, the one that belonged to Chancellor Bismarck.

On one hand, part of Bismarck’s foreign policy depended on the newly formed Germany to be in an integral position in the world politics via cordial relations with major powers and “soft” interventions to international crisises (ex. their mediation in the peace table helped Ottomans keep much of the Balkan holdings on their hands while also satisfying Austria-Hungary and Russia through key conquests like Belgrad). In this regard, Germany could very well form a cordial and maybe even a beneficial to both sides relationship with the British Empire.

On the other hand, this foreign policy also avoided any long term commitments with any major country, destabilizing any block of power that may exist, so that no concrete coalition could ever be formed against Germany, preventing the chances of a major war across Europe that could end with Germany ending up as the loser. While WW1 was inevitable at some point due to imperialist competition, Bismarck at least sought to minimize the fighting in any way possible.

So, to answer your question, while Wilhelm II made an archnemesis out of the one country it didin’t have to, Bismarck wouldn’t make it an ally either.