No. Every even x even rectangle has equal dark and light squares. Every even x odd rectangle has equal dark and light squares. Every odd x odd rectangle has

No. Every even x even rectangle has equal dark and light squares. Every even x odd rectangle has equal dark and light squares. Every odd x odd rectangle has one more odd then even, or one more even then odd. (1x1 square is obvious, any odd x odd rectangle can be reduced to 1x1 square by removing only odd x even rectangle.) Since the T piece creates a odd-even difference of 2, any number of other tetris pieces (including repeats) that only contains a single T piece can never form a rectangle with no holes.