Will eM Client work on the new Microsoft Pro X with the ARM processor?

The Surface Pro runs Windows 10, so yes, it will work.

I was worried because I have been reading some articles that have said the processor is an ARM processor and not your normal Intel or AMD so some programs/apps will not work.  

The biggest limitation is that x64 applications wont work. x86, ARM32 and ARM64 are all compatible, and as eM Client is an x86 application (32bit), it should be fine.

It might be a case of install it and see what happens.