Um, no, this doesn't follow at all.
Traditional conservation (as in those guys in safari suits playing at 'park ranger', the petit bourgeois birdwatchers, etc) tends to see nature as something seperate from humanity, which needs to be fenced in and 'conserved'. Living in 'balance' with nature in this view means seperating out the natural areas from the human areas, and attacking each if they try and break the barrier.
A good example in South Africa is the Kruger National Park, where on the one hand, people living in the area were deprived of their land to form the park, and on the other hand, rangers have carried out periodic kulling operations to try and stabilise the ecosystem (in a fairly crude, and often counter-productive, way).
Deep ecology, on the other hand, sees humanity as inseperable from nature, and advocates the perspective of ecology (with its focus on population control, complexity, etc) as a perspective for dealing with society. I.e. 'nature must take its course'. This is more akin to the perspective people like Peter Singer are talking from. In a sense deep ecology is a reaction against the seperation of human and nature in conservationism (and conservationism's liberal cousin, environmentalism).
'Green' ideas tend to draw from varied sources (depending on which 'greens' you are talking about) - deep ecology is certainly an influence, as is (in some cases at least) a concern for social justice (defined in all sorts of different ways).
Peter P.S. does the WSM still believe that we'll get socialism by the workers voting for it? -- Peter van Heusden : pvanheus at hgmp.mrc.ac.uk : PGP key available Criticism has torn up the imaginary flowers from the chain not so that man shall wear the unadorned, bleak chain but so that he will shake off the chain and pluck the living flower. - Karl Marx
NOTE: I do not speak for the HGMP or the MRC.