Yes I fill mine out and I am sure I put several rounds through the new gun to make sure everything is working correctly. And usually if there is something seriously wrong with the gun it will be evident. And you can get it repaired or replaced.
If you do not fill the card out and the gun should have a year or two warranty or you do not at least check it out by firing it you are on your own. And if it has a lifetime warranty and your purchase documents are not on file you may have a serious problem if you have problems.
Keep in mind even with a lifetime warranty it usually only covers defective parts and factory labor. It does not cover normal wear on parts and etc.
The Constitution is not an instrument for the Government to restrain the people. It is an instrument for the people to restrain the Government!
Today, we need a nation of Minutemen, citizens who are not only prepared to take arms, but citizens who regard the preservation of freedom as the basic purpose of their daily life and who are willing to consciously work and sacrifice for that freedom."
-- John F. Kennedy