My answer (and that of many past clients) would be no.

Unless the person is a 'green' fanatic with pre-existing ideas on
sustainability and the environment, then most people are more
interested in price and then quality.

Most people don't know if their timber skirting came from managed
forrests in Sweden, of illegal logging in Canada. They don't know that
the paint contains many VOC's, only that it smells a bit. They don't
know that the process of making bricks, blocks and cement is very
energy intensive, and that a timber frame and cladded structure is
available. They don't know that there are other insulation products
which will keep them just as warm, but are easier on the environment to
produce.

If the difference is having a more environmentally friendly extension,
or some chrome switches and nicer wall tiles and bathroom suite, then
the later wins almost every time.

dg