As ever, all we can do is speculate! I can see the logic of arguing that Waitrose (as opposed to, say, Aldi) would take business away from our local butchers, delis, the fish stall, etc. On the other hand, look at this article about Cheadle Hulme:
http://cheshire.greatbritishlife.co.uk/article/a-choice-location--we-visit-cheadle-and-cheadle-hulme-39666/The key sentence is a quote from Pimlott's, the long-established Cheadle Hulme butchers, which now finds itself across the road from Waitrose: 'The coming of Waitrose to the centre of the village has helped keep us busy, because local people tend to shop locally.’
The truth is that it's a complex issue and it's very hard to predict what will happen - there are so many variables. But what Pimlott's in Cheadle Hulme have found, I think, is that although they may have lost some business to Waitrose, that is more than compensated for by the greatly increased footfall in Cheadle Hulme centre which Waitrose has brought. If having a proper supermarket in Marple stops the weekly exodus to Bredbury, Hazel Grove etc for supermarket shopping, we could find the same happens in Marple
But for me, the big downside of the Trinity Street/Chadwick Street scheme is that (despite Kirkland's protestations to the contrary) it will not help the college deal with its poor-quality estate.