I mean, it's a coincidence but I don't see why it's particularly strange. Some familiar numbers, when combined, are similar to another familiar number. If you play around with enough familiar numbers you're bound to find all sorts of coincidences like this
(By the way, accelerating at g for one year wouldn't leave you at the speed of light, it would leave you at 1.03 times the speed of light. Accelerating at g for about 354 days would leave you right at c. It's not an exact thing.)
As Astro_Robert began to talk about, though, there are a lot of reasons why this has nothing whatsoever to do with physics. For one thing, what we call g is only the gravitational acceleration on the Earth's surface. The acceleration would be lower at higher altitudes and higher at lower altitudes, so if you were actually accelerating at g, it wouldn't be very long at all before the acceleration you felt became very different from its surface value (9.8 meters per second^2).
Second, this calculation doesn't take into account relativistic effects, so if, say, a rocket ship were accelerating at g for a full year, it would most certainly
not reach the speed of light. The reason is that according to relativity, as you start moving, you effectively gain mass from that motion (you have kinetic energy, so think E=mc^2, although that equation isn't quite the relevant one here). Now, you can't apply a constant acceleration, you can only apply a constant
force. Recall that force is dependent on both mass and acceleration (F=ma), so if your mass is constant, then so is your acceleration, but if you're getting heavier, then the same force will accelerate you less and less. So if your rocket ship has a constant force of mg (where m is the rocket's rest mass), then as it gets faster, the actual acceleration you feel will be less than g. As it turns out, this constantly-shrinking acceleration approaches a limit - it means that no matter how much force you apply, you can get arbitrarily close to but never reach the speed of light