Yes, your account will be billed twice if you upgrade your plan before the end of the existing billing cycle, but all unused days of service will be deducted from the price of the new plan. Your subscription will continue to follow the renewal date of your existing billing cycle (renewal date).
Be aware however, that consumed credits from the previous plan will also be deducted from the credits of the new plan.
To receive more details on how an upgrade is calculated, please check the following guide.