I can't really give you medical advice if you're on a low-sodium diet, but pasta cooked in salted water definitely absorbs some of the salt along with the water. That's the purpose of salting the water: to season the pasta throughout. You can reduce or omit the salt if you think you need to, but your pasta will be less tasty.
If you really want to science it up, you can calculate the concentration of the salt in the amount of water you're using (weight of salt / weight of water), then multiply by the difference in the weight of the pasta before and after cooking (the amount of water absorbed). That should give you the approximate amount of salt absorbed by the pasta. 40% of that is the weight of the sodium in table salt (NaCl). I think you'll find that it's a lot less sodium than you would get from consuming processed food, and is not likely to be a health risk. However, if you need to measure the exact amount of sodium you're taking in, that's the way to do it.