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 is no longer offered and you need a CPU that supports the SSE4.1 instruction set. Only very old CPUs don't support it.
From Corona Renderer 3 onward, the Licensing Server and the DR Server 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).
From Corona 12 onward, you need a CPU that supports the SSE4.2 instruction set. Only very old CPUs don't support it.