The process will be in blocked state. The term "blocked" doesn't mean unavailability of resources - it just means that the job is blocked from using the CPU.
Whenever a job initiates an I/O request, it won't be using the CPU for that time. It's the job of the scheduler then to find another process which can run during the time when the former job's I/O is being serviced. When the I/O is finished, the job then signals an interrupt to the operating system and the scheduler decides what has to be done next.
EDIT: Doesn't the hardware require usage of the CPU?
No, it doesn't. Whenever the CPU issues an I/O instruction such as reading from a hard drive, the request is processed by the hardware/device controller, which is a specialised chip present on the hardware.
"Originally these were simple chips that performed specific operations for the CPU, but modern hardware controllers are basically their own microprocessors with firmware and everything, so they are capable of very complex operations without the main CPU's help. The controller is able to read and write directly to and from system RAM using what is called a Direct Memory Access (DMA) controller, a special chip that transfers data from the hardware controller to main RAM without the CPU needing to do anything. Thus, the CPU does not need to micromanage all tasks involved with I/O. At one time this used to be the case, but these tricks (interrupts, DMA, special controllers) were invented in order to improve CPU performance and make things a lot more efficient."
Source: https://stackoverflow.com/questions/13596997/why-is-the-cpu-not-needed-to-service-i-o-requests