The short answer
Yes, for a meaningful range of strength and muscle development — especially for beginners and intermediates. Muscles respond to sufficient tension and effort, and bodyweight exercises can absolutely provide that.
Where it genuinely gets harder without equipment
Progressive overload becomes trickier once basic bodyweight versions get easy — you can't simply add 2.5 kg like you would with a dumbbell. This is where variations (single-leg squats, archer push-ups, weighted vests) become necessary.
How to keep progressing with just your bodyweight
Slowing the tempo, adding pauses at the hardest point of a movement, increasing reps, reducing rest, and progressing to harder variations (regular push-up to decline push-up to one-arm progression work) all create genuine overload without external weight.
Where it eventually hits a ceiling
For advanced lifters chasing serious strength or size beyond an intermediate level, external weight eventually becomes necessary — but that ceiling is genuinely much higher than most beginners assume, and most people never actually reach it.