Is it possible to replace a CC2500 with a CC2531?
All of the Chipcon stuff that TI has is more or less interoperable within frequency bands, so you shouldn't have any problems. When I hear "Arduino" I assume entry-level knowledge (sorry for the presumption), so please understand that there's 20 or so different registers you'll have to configure to get these things talking to each other, and if you don't have RF equipment laying around, you may have a hard time being able to debug incorrect register values. TI's SmartRF Studio is excellent, though, and you shouldn't have any problems getting it working if you're a competent embedded developer.

Having said all that, I'm going to interject my personal opinion and note that I absolutely despise the SoC versions of the CC chips. They use an industry-standard 8051 core design, but don't get your hopes up -- a lot of the tools and libraries force you to use IAR, which is the biggest waste of $5000 imaginable. 

I've found that the SoC versions of the radios usually aren't cheaper than a stand-alone CC-radio + general-purpose MCU. As an example, the USB-enabled PIC16F1454 could easily talk to a CC2500, and it's on the order of $0.80-$1.00 each. 

Food for thought.