Norwegian Wood

I have just bought a copy of Haruki Murakami's Norwegian Wood. The cover spiel tells me that

When he hears her favourite Beatles song, Toru Watanabe recalls his first love Naoko...

but does he - and already this is the only question on my mind - does he, when thinking about her, get Norwegian wood? And would that pun work in Japan (where the novel's title must have been the same?) - or is it not close enough to the bone?

I shall read, and find out.