Deep cleaning will loosen your teeth only if they are supported by tartar or calculus and have lost the natural bone ,gums support,not otherwise.
But if nothing is done the teeth will keep on loosening and gums support will be permanently lost leading to shaking teeth in future.
Next Steps
Ask about severity of ur gum disease to ur dentist so that u know exactly what will happen post cleaning.
Health Tips
Do not delay the treatment with fear of loosening teeth,there are ways to tighten them.