I'll just come out and say I'm a member of the St. Petro Mohyla and St. Demetrius of Rostov fan club.
There was considerable western influence in present day Ukraine before Peter the not so Great. You can see it in art, architecture, music and education. Some was not so good I suppose, but some of it had a great deal of value and helped the church after it was cut off from Constantinople because of the Turk. The Ukrainian clergy, brought much of this in to the Muscovite church starting in the 17th century.
Much of that happened before Peter the not so Great ascended the throne. His real goal was to co-opt the church from within and to exercise control over it. His aims were political. There was influence from western Europe at the time throughout Russian society; some Catholic but more of it freethinking and/or Protestant. The dissolution of the Patriarchate for instance was based on what he saw in Scandinavia.
It seems like many of the Anti-Western Orthodox love to harp on this period. It's too bad in my opinion.