Yes it does change - larger needles make larger stitches so there's less of them in 4". Smaller needles produce smaller stitches and there's more of them in 4".
The gauge and needle size on the label is mostly to fit a yarn into a weight class and so you can substitute yarns easier, you might not actually get 18 sts in 4" yourself on size 8s, you may get 17 or 20. And a pattern with the same yarn might not use the same needle, or have the same gauge so you'd use whatever needle matches the gauge in the pattern.
The best method to use is to knit a sample and see what you get, there really isn't a formula. CO about 20 sts with the 11s and see how many stitches you get in an inch or 4". I usually get 3 sts per inch with worsted on 11s, you might get more or less depending on if you knit tighter or looser than I do.
You'd need less stitches, so if this is for a sweater, you'd have to figure out which smaller size you need to knit to make the finished measurement come out the size you want. If it's a hat or scarf, multiply the width you want times the sts per inch to see how many sts you need.