From my experience I would say a HUGE yes. Here is what it did to me in my current game where I am Elizabeth of the British Empire on Noble, the map is a Large Archipelago.
I started and went for Hinduism and was able to found the religion, once my borders expanded I was able to see across the water to a continent to my Northwest and another to my East. Caeser was to the West and Catherine to the North. My religion started to spread to their cities once open borders were established (yes over water ways as I never even stepped foot on there islands!). But Catherine decided to make her people follow the Buddhist faith, and from then on our relations detiorated pretty rapidly.
I had since expanded a good bit and found that I was the only one on my island and that it was a pretty large island, only bad thing was I had NO copper and NO iron and no matter how good my relations were with anyone no one would trade some with me so that severely restricted my military and decided to try and tech my way up to some redcoats. About the time I got redcoats Catherine declared war on me and brought Saladin into the fray with her. Saladin was on the opposite side of Caeser so I bribed him to go to war with Saladin so I wouldn't be bothered with both at once. I then started to build of some defense expecting an attack since she did declare war on me but it never came. So I took it to her and kept ferrying redcoats back and forth to her continent.
I was taking some heavy losses and decided to take some defensive units away from my cities and ship them out. The city that was the least defended was Hastings on my East coast right by my capital of London. Without a source of Iron my navy had fallen behind and I was not able to build frigates, but Catherine was and boy did she ever. She didn't attack with just one or two frigates, it was an entire navy! My caravels and galleons didn't stand a chance and my navy was no more. Then the next thing I knew there was a stack of about 15 units right next to Hastings (and this was even after my rag tag navy somehow managed to destroy at least 4 of her ships). They took Hastings with a small fight and moved onto London. But thankfully I had just learned the tech that allows machine guns to be built and was able to upgrade 3 units (who had city garrison II, and London had 80% defensive bonus). They were able to repel the largest majority of the attack and then I just had to mop up the rest and take back Hastings. The only reason I was able to do fight back was a little bad timing on her part, just ONE more turn and I would have been a goner for good. If I would have lost London that would have taken away my Holy City (and all the profits from that), my greatest production city, I would not have been able to create destroyers and then repel her next invasion (was even bigger than her first) and for the most part she would have just rolled over me since I had neglected city defense for the most part in the Southwest of my island.