The short answer is yes. If you don’t salt the pasta water the whole dish will taste under-seasoned, that is a fact.
There are many different recommendations out there on how much salt to use, 1 ½ to 3 tablespoons per pound of pasta. Many chefs, however, use the “it should taste like the sea” rule of thumb.
Some say that the salt should be added when the water boils and some add the salt into cold water so that they won’t forget the salt.
Clearly what amount to use is subject to personal preferences and only experience can guide you on what is right for you.
What type of salt should be used?
A variety of people claim that ionized salt will create metallic flavor and thus should not be used.
Sea salt, table salt kosher salt, will work fine and as usual only you know what you like so to find out a little bit of experimentation is required.
Also, think about the salt amount with regard to what you will eat together with the pasta, for example, if the sauce is salty or not, and adjust accordingly.
To summarize, pasta cooked without salt in the water will taste under-seasoned. Think about what the pasta should provide to the sauce and adjust the amount if needed and learn what the water tastes like and how the pasta comes out as a result and develop your own preference.