The vocal folds (commonly known as vocal cords) are not muscles, they are mucus membranes, so technically, you cannot "strengthen" them as you would strengthen a normal muscle.
But yes, singing and vocal warm-up exercises will definitely help them stay loose, and training them the hold different notes will certainly make you a better singer and get your vocal folds used to that type of use. Just don't overdo it! Folks like professional singers, sport coaches, auctioneers, and radio announcers, etc, can have lots of issues with their vocal folds growing vocal nodules, which result from over-use. These nodules can impact the tone and quality of your voice, and may likely need surgery to remove them. So train your vocal folds well, and warm them up well before singing, but don't overdo it!