Of course it does depend if you are doing other things while it is calculating in the cloth room. If you are browsing the internet (or even playing some game) then a dual core will improve performance. One core will be calculating in the cloth room and the other core is available for other things, as long as you have enough memory available to prevent swapping. A dual core will be used completely when rendering to the extend that response from the computer can be very slow and some programs (like email) may report connection loss while using an internet connection.

As usual in computing everything is about finding the right balance. Increasing the number of cores will soon lead to another bottleneck (like not enough memory). Fixing that one will start the cycle again. You can never have enough processing capacity, memory, hard disk space, screen real estate, etc. when working in 3D.

Beware that replacing the processor may require upgrading the BIOS on the motherboard. Take care that the new processor is completely compatible with you existing hardware (including motherboard, memory, video card and power supply). The number of times I had to replace half the computer for a simple upgrade (or replacement) of one component are way beyond my capacity to remember (I don't do this for a living but do support several people). Cooling is very important. A better processor produces more heat and often heat causes many problems and these problems can be hard to trace.
Before replacing a processor first make sure you have enough memory (2 Gb). A memory upgrade has way more impact than the processor.