I'll preface this by saying I have a limited knowledge of hydraulic accumulators in general. Increasing the pressure won't make it work "faster"- it'll increase the pressure that the accumulator will provide when needed.
If it's charged at 1000 psi, it'll give 1000 psi back to the hydraulic system when called upon. If it's charged to 1600 psi, it'll give 1600 psi when called upon. It's similar in to a pressure tank in a well water system.
If your hydraulic pump is 2000 psi and your accumulator is charged to 1600 psi, you'll have 2000 psi in the accumulator when the pump is running but the accumulator will exert 1600 psi on the hydraulic fluid when the pump isn't running.
If it's charged at 1000 psi, it'll give 1000 psi back to the hydraulic system when called upon. If it's charged to 1600 psi, it'll give 1600 psi when called upon. It's similar in to a pressure tank in a well water system.
If your hydraulic pump is 2000 psi and your accumulator is charged to 1600 psi, you'll have 2000 psi in the accumulator when the pump is running but the accumulator will exert 1600 psi on the hydraulic fluid when the pump isn't running.