Whether wearing climbing shoes that are too big, or bigger than the actual size you need, is ok, depends on your goals and the reason why you are wearing shoes that are bigger than you need.
Many climbers have shoes that are specifically for warming up on easier routes. This allows them to get their feet a little bit warmed up and ease into wearing the smaller and tighter climbing shoes. It also allows them to climb more comfortably without the feeling of pain or discomfort that comes with smaller climbing shoes.
For warm up routes, it's normally ok to wear bigger shoes, as you probably will not need the precision and performance of the smaller and tighter shoes. If you are planning on wearing bigger shoes for harder routes, or for projecting routes, you may have a hard time as the bigger and looser shoes can reduce your performance, especially if you are working on hard routes with small foot holds that require a lot of precision and the ability to apply a lot of force to your toes or heel.
In the end, it really comes down to experimentation. Experiment with different shoes and different sizes, match them to your goals and purposes, and find what works best for you.
