Try this yourself. Get instances on each of the providers in question and see what choices you have.
In general, the answer is no. Rent a computer IaaS does not give you a choice of specific CPU models. Maybe the microarchitecture is known. Especially for the common instance sizes, the provider may substitute AMD or Intel for x86. This is primarily for their supply chain diversity, branded as giving you choices. Google's E2 series could be on any of 4 microarchitectures, for example.
Although sometimes, specific CPUs are name dropped. Consider Azure's large Mv2 on Xeon Platinum 8180M. 416 vCPU is such a specific number but would fit well in 8 sockets of 28 core processors. Some scale up database customers are betting (a lot of money) on this specific processor. All the branding is not a guarantee the instance type is static, but there is no obvious substitute anyway.
i7 is not a server processor, and the big three clouds you named are not interested in it. Presumably because it does not support sufficient memory and CPU density to scale.
If for whatever reason you do need a desktop processor and can't host it in your computer closet, ask sales of some hosting providers to accommodate. Consider colocation service where you provide the hardware and they rack it.