Also what of the notion that the Kremlin actually killed him out of jealousy over his fame?
Not sure that's a good reason for killing him off. Essentially, what fame Yuri had could be attributed to the Kremlin and their pursuit of the space program. He's beneficial to Soviet image during the Cold War and it's hard to see him killed because of his fame. Had he shown indications of criticizing the space program or Soviet practices, then we get into plausible reasons.
But on topic: it probably worked in favor of the Soviets that the Americans wouldn't admit him. Had the Soviets pushed an American visit more, it's likely he could have gone, but still wouldn't have made it to the Whitehouse. I'm willing to bet the Gagarin's tour was at one point considered for a stop in America, but after some light apprehension from the Americans, the Soviets completely dropped the idea and let America look like the intolerant party here.
The implications are that if Gagarin is allowed in the States, and possibly meets with Kennedy, there could be some degree of future cooperation between the American and Soviet space programs. Not immediately of course, but a situation where Gagarin meets with American astronauts in the U.S. could be used as precedence and fuel for international cooperation. It all depends on how the rest of the Cold War turns out, because it can easily prevent any effects from such a visit.