The simple answer to your question:
YES, your landings do matter!
Now for the more complex answer:
Your landings are a good indicator of your ability to absorb force and/or power. A "heavy" landing that is loud (usually this involves the heels hitting the ground hard) shows that you are not able to properly absorb the force you are landing with. Why is this important? Well think about this, would you jump higher if you squatted down, paused for 5 seconds, then jumped? No, of course not! This is because the ability to absorb power is strongly tied to the ability to produce it.
Here's a simple test you can do:
1.) Measure your standing vert.
2.) Now stand on a box that is about half of that (so if your vert was 30", stand on a box 12-18"). Do a depth jump off of that box (drop off it, quickly absorb the landing and jump less than 1 second after you contact).
If your vert off the box is less than your vert from standing, you need to work on your power absorbtion.
I think the easiest way to do this is through altitude landings. Start off with a box that is about as high as your max vert, step off and absorb the landing. Your goal should be to make it as quiet as possible. Increase the height until you can no longer land quietly and/or keep your heels off the ground. I would recommend landing in two different positions, a full squat and 1/4 squat (which is about the depth you would squat down to jump from). Obviously you will use a higher box for the full squat landings than for the 1/4 squat landings.
I would do 3 sets of 5 with each type of landing (10 seconds between reps, 120 seconds between sets). Then about 20-30 more moderate intensity jumps (box jumps, broad jumps, vert jumps, etc) in 2-4 more sets.
Go for 3 weeks where you really focus on improving your absorbtion skills (so if you lift 3 days a week, 2 days would be the plyo stuff, the other day, whatever), then take a week off and test your vert on the 5th week. I wouldn't be surprised if you can get an extra inch or so doing that.
I'd like to see some of the other "jumping" guys (climon, coolcolj, jumanji, ze, thebodyguard) "jump in" on this subject. Get it... "jump in." ha... ha...