Sort of.
Physical fitness for good health has 2 components: aerobic fitness and strength. You can improve your aerobic fitness and your upper body strength at home (rings and/or handstand pushups are enough for all but the most advanced strength athletes).
Core/lower body strength is another matter entirely. People tend to quickly progress to 1x body weight squats and deadlifts. And someone who is more advanced will probably be in the 2x-3.5x range. Without access to serious weight, lower body training is usually pretty ineffective, strength wise.