The more questions you answer, the larger your sphere's surface area becomes--which means that simply by answering questions you will be able ask an ever-increasing number of questions built upon the answers to the previous questions. In that sense, yes, I agree with James that things become more interesting the more you know about them. The fidelity, if you will, of the questions becomes greater with each successive 'generation' of inquiries--that, to me, makes the inquiry more interesting.
But enjoyable? Fulfilling? Rewarding? Those are totally different questions (not sure if those facets were represented in your own query, but they seem like next door neighbors to 'interesting' in my way of looking at things). And honestly, when it comes to whether or not greater understanding leads to greater enjoyment...no, I don't think that knowing more about a thing generally makes it more enjoyable, or fulfilling, or rewarding.
As the fidelity of one's inquiries increases, the price (it seems to me) is that the sense of wonderment and awe which accompanies all junior-grade Eureka! revelations diminishes at a directly proportionate rate to the (increasing) fidelity of the inquiry. Famed physicist Richard Feynman, if memory serves, had a quote which hit me like a Mack truck when I first heard it (relayed by Laurence Krauss, who I generally don't care for), and it goes something like 'Any question based on the word 'why' is not really a 'why' question--it's a 'how' question.' Can't seem to find the video where Krauss quoted him...think it was a panel at a science communication convention, featuring Neil deGrasse Tyson, Bill Nye, and a few others.
Basically, what I understood Feynman to be saying is that if you ask a question with a 'why' like 'why is the universe here?' what you're really asking is 'how is the universe here?' Slow learner that I am, it took me awhile to wrap my mind around that one. But in the end I think, in terms of intellectual inquiry, he's probably right: when it comes down to it, every inquiry will eventually become a nuts-and-bolts examination of how a thing is, rather than any query like why it is.
It seems to me that the question of 'why' is a much more human question than the question of 'how.' 'How' is a cold, methodical, mechanical question. 'Why,' on the other hand, is one which seeks not only accuracy, but truth (and beauty) as well. Eventually, after sufficiently discrete and effective inquiry, the opportunities to ask 'why' diminish until they're all but gone. To a scientific mind, this is not a problem in the least. Indeed, it would be preferable to Mr. Spock if all inquiries became simple intellectual exercises in the application of the scientific method (or some superior version of methodical inquiry).
And no, I'm not suggesting that scientific inquiry cannot yield awe or wonderment. I'm saying that the opportunities to experience such during an inquiry diminish the more you know about a given thing. And, to me, that generally makes a thing less enjoyable. More interesting? Probably--especially if it's something which held my interest at the outset of my inquiry--but 'interesting' is sometimes less preferable than 'inspiring,' 'breath-taking,' or 'humbling.'