I think it would be the other way around. Patkul would find little support for his plans for a grand coalition against Sweden at Saint James in London (since England-Scotland is the major country, that is where the court would be). Everyone was holding their breath in western Europe, waiting for the death of Charles II of Spain.
Patkul wanted Saxony, Brandenburg and Denmark-Norway in his alliance - August of Saxony agreed, but his word was never worth anything, he broke any agreement he made if it suited him. Brandenburg refused, and I Anne and George would be interested either - with England-Scotland and Denmark-Norway united, Denmark-Norway would be aligned with England-Scotland and the Netherlands.
Patkul might very well give up on his attempts to form an alliance against Sweden if Denmark-Norway refuses and not go to Russia. Then Peter the Great will continue his original plan to attack the Ottoman Empire.
This will probably mean that Denmark-Norway is allied with England-Scotland and the Netherlands in the War of the Spanish Succession with Sweden friendly (hiring out its German garrisons to the Dutch, English or Danish, as it had done before).