Yes, but you cannot assume that at any setting the hot water from the pump and the mains water will be balanced unless you add equipment to enable that.
the setup I am planning has a two bar single pump on the hot supply, a pressure reducing valve on the cold - set to two bar, all connected up to a thermostatic mixer shower - Should I be adding something else to the equation?
I've already answered your question. You need a pressure equalising valve, also known with similar names.
Google it. They're only about £35.
You do NOT need a p reducing valve on the mains.
What's the matter? You waiting to be told your idea is great? Forget it, it doesn't work properly. I know because I've seen and done it dozens of times.
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