A one month lockdown would do very little to benefit nature. We've seen it ourselves - most of the news stories showing nature 'coming back' have been debunked as fake news.
The timescale for nature to recover is not a matter of months, but years, even decades. For example: many whale populations are recovering since the whaling ban in 1982, but 40 years later many populations are still not at their pre-whaling populations size. Even if you had a month each year of lockdown, a forest won't recover if there is poor conservation management in that area the rest of the 11 months of the year.
I think it is tempting to look towards dramatic solutions that seem like a panacea, but I don't think it is helpful to promote impossible to enact (and probably not even beneficial) solutions.