Yes, Sandy-Wroe, they could, because I have just such a condition with just such a cause. I was first diagnosed (after a very cursory locum GP examination) with RSI, but then a physio and my own GP diagnosed Carpal Tunnel Syndrome. We've tried steroid injection and that didn't work, and I'm now waiting for a hospital appointment.
Meantime my boss found how I could refer myself to Access to Work and get some help with ergonomic office equipment. They sent a physio to visit me at work to make a workplace assessment. That was last week, and her report should be through any day now. She was very thorough, talked about my job and the work environment and made lots of measurements, and said she will probably recommend a vertical mouse, split keyboard and separate number pad, as well as a deeper chair, because I'm tall and the seat pan on mine is too shallow. Re. the mice, she mentioned two types - the Evoluent Vertical Mouse and the Quill Grip-Less Mouse. You can find both if you Google them. They're not cheap, but Access to Work can provide grants for your employer towards the cost.
She did also say not to use wrist rests. Latest research is that we tend to get lazy and use them when we're typing/mousing when, in fact, they're only designed for actually resting on. What they do, apparently, is to further compress the nerves and blood vessels in your wrist. What we should be doing are exercises to strengthen the wrist.