To answer the question, purely in terms of shape alone, I'd connect the rectangle with a textfield (editable or otherwise), and the rounded shape more with an action like a button. Search boxes are indeed often rounded and frequently combine multiple elements - they are like some special case of editable area and action area.
My interpretation is almost perpendicular to your question of whether one shape means editable or not, in that I find neither to be the case and actually observe an alternative meaning instead.
To combine your intended meaning with mine would be very confusing and yours would be likely lost in translation.
However, in a mobile world where the content is the interface and where there should be an increased use of natural user interfaces based on human intuition, I would say that putting a border round read only content is unnecessary and preferably avoided. (I realise that's something of a generalisation.)
Read only content is simply: content.
By asking this question you're almost giving yourself the answer: You're much better off using accepted mechanisms already familiar to others.