Up to Corona Renderer 1.7 hotfix 2 - no, you can also use a processor without SSE 4.1 and Corona Renderer will run the Legacy version which is about 20% slower.
From Corona Renderer 2 onward, the legacy version will no longer be offered, and you will need a CPU that supports the SSE4.1 instruction set (that is, any processor from within the last 10 years). Here is a list of compatible CPUs.
From Corona Renderer 3 onward, the Licensing Server and the DR Server will no longer support CPUs without the SSE4.1 instruction set and are now 64-bit only applications (they will not run on 32-bit versions of Windows).
If you wish to run Corona Renderer on a CPU, which does not support SSE 4.1, you can download Corona Renderer 1.7 or older here: https://corona-renderer.com/download/old