Will teeth crowding cause teeth to feel loose?

No. Not in and of itself. Many people with severely crowded teeth have strong healthy teeth and supporting tissues (bone and gums). However, crowded teeth are definitely more prone to cavities and periodontal (gum) problems. Along with traumatic occlusion and loss of bone, the teeth may become loose. If your teeth do feel loose, see your dentist to determine cause and remedy.
Yes. The more crowded teeth are, the more overlapping of teeth. They continue to cross over at increasingly lower position, away from the top of the teeth. As a result, the gum gets pushed down lower, to which the bone also responds by moving down. As the teeth move into more crowded position, the bite changes and create traumatic pressure. All that--bone loss and heavy bite--causes teeth to loosen.