To use a higher solid content of adhesives then the production speed will be increased, is it true ?

The answer is not really.

Popularly, the water based Acrylic adhesives manufacturer may offer you the solid content between 50-65%. It seems, if used higher solid content, thus water contents will be less, the production may be increased ?
In fact, the drying speed of a coating line, which not only concern the water contents but also need concern viscosity and vaporization of adhesives.

Definitely, more high viscosity glues will be more difficult to dry out the water. When coating the same solid content glue but different viscosity, then the lower viscosity glue will be dried fast, i.e. production will be fast.

Therefore, if who would supply you a higher solid contents glues, then you should also study its viscosity at first.
(Remarks: do select a low viscosity glue first, then take a higher solid content as possible.)