Simple answer is no.
RNP is 'required nav performance' in a lateral sense, at the moment anyhow. My assumption is that you're refering to RNP 1.0 and not RNP 0.1 (often defined as RNP <0.3). Either way there isn't any VNAV reuirement, unless you start looking at intricate and specific approach requirements that utilises these lower RNPs.