Yes, any mode of exercise will contribute towards weight loss by increasing energy expenditure.
However, the calorie-burn is quite modest. Most weight loss will stem from better food choices.
Where bodyweight exercise (or any other form of resistance training) becomes particularly useful is dictating where the weight is lost from. Fat stores or muscle stores!
Bodyweight exercises, performed to a high degree of effort, build and preserve muscle. This means your body must turn to stored fat reserves to make up the energy shortfall.
In other words, bodyweight exercises help prioritise fat loss as you lose weight.
This is really useful. Keeping hold of your muscle will keep your metabolism firing, improve your body aesthetics and prevent rebound weight gain.
A triple bonus for effective weight loss!