Thankfully, it is just a myth that hairspray causes hair loss. This is because hair loss has much more to do with the follicles under the skin than the hairs themselves. However, there are many real reasons for hair to fall out.
Since hairspray is applied to the hair shaft, the part above the surface, it should not have any lasting effect on the growth of your hair. However, it can become a problem if you aren't washing your hair regularly.
There is no real danger to using hairspray. Even daily application is not harmful. Just make sure you are consistently washing your hair with shampoo to avoid any buildup that could become unhealthy.
In the same way that hairspray can't make your hair fall out, it isn't going to help it grow either. At least, not biologically. But while hairspray may not make your hair thicker, there are certain sprays that can make it appear that way.