The thing about Anglo-British monarchy is that, from any period when we've heard of Russia and vice-versa (post-Muscovy Company), they can't just marry anyone. They're part pf a complex political system - the commanding part, often, but still a part.
Look at the enormous tensions over James succession: arranging a personal union with a country next door that spoke nearly the same language and belonged to broadly the same branch of Christianity, and whose coming into possession was obviously beneficial to English policy, took years of secret correspondence and a lot of money. Look at the storm the Stuarts raised whenever, for reasons of sober foreign policy, they tried to marry Catholics.
About Russian modernisation:
Peter the Great was undoubtedly a towering figure but in my opinion he proves, like the Meiji Restoration lads, that the way to be remembered as great modernisers is to be the people who start to dress like members of the English-speaking upper-classes. And like Japan, Russia has a decades-long process behind its 'sudden' emergence in the great-power game.
What did Peter actually do? The substantial reforms he made were establishing a new model army and the infrastructure to support it, building a navy which Russia probably didn't need, importing a lot of expertise to do these things, finishing the bludgeoning of the church into submission by the monarchy, creating the service-noble class - and consolidating serfdom, which we in the west like to see as an age-old symptom of the backwardness he supposedly worked against.
These are changes in organisation, not underlying potential. Russia remained what it had been: a poor peasant country, but one big enough to pool formidable resources.
His foreign policy achievements were certainly impressive, but they all reflect long-term trends. Russia had won the last round with Sweden on points (the really astonishing thing about the GNW is how long the Swedes lasted: last time they got the worst end of a draw against the Danes all by themselves); had long been outstripping Poland; was bound to consolidate its control over Ukraine sooner or later, since neither Poland nor the Ottomans were strong enough to be rivals in the area; and hadn't even been involved in the earlier capture of Azov by the Cossacks acting alone.
Peter created an efficient instrument for doing things Russia was equipped to do: when he did what it wasn't yet equipped to do and invaded the Balkans, reality intervened. That the Russian were equipped to intervene in Germany - which had been true since Poland ceased to count - caused Britain, France, and the Netherlands to start taking them seriously (one finds in the western responses to Peter a nice parallel to Japan later and perhaps China today: "They're becoming like us! Hurrah!"/"They're becoming like us! We're doomed!"), however. If we'd been terribly foresighted, we'd have started earlier. I think Russia could have played the 18th C power-game without Peter - perhaps not so well, since the system he established and his successors proved very well-adapted for the job that century, but played it, certainly. I mean, it's difficult to change the fact that Russia's neighbours are also poor peasant countries, but one's actually tiny, one's politically moribund, and one's overstretched and far away.
And then it could start the 19th C power-game on a not-dissimilar footing. hell, not having Poland proper is probably a plus. That won't change that fact that Russia ain't the place to start the industrial revolution. After all, railways weren't a state-secret with us. Calling them into existence by fiat is a huge ask and only works when they're immensely strategic and symbolic (Can-Pac, Transsiberian - the latter built only once Russia actually had railways west of the Urals, note): you need a civilisation that can support them. And was Russia so late? Germany and Japan, great modernisers, we are told, started the industrial boom a matter of decades before her - and remained countries with a very large peasant element.