Hmm. I'd think there'd be some tension on the subject. In general the Imperium rules the space between planets so that would give planetary leaders the latitude to make whatever ruling they choose.
That said, within the Imperium itself you'd probably have competing interests. Corporate groups after planetary resources would want to discount this kind of philosophy. For the most part they do seem pretty cutthroat and ruthless in the Traveller setting.
On the other hand, you seem to have a sense of stewardship on the part of organizations like the Scouts and for every noble primarily motivated by short term profits, via corporate connections, there may well be one operating under noblesse oblige and backing interdictions, in some cases, and other less drastic controls with an eye to long term resource management, sustainability or other economic/political considerations.
The Vilani culturally are probably most far sighted and bound up in the concepts of noble action. They've had plenty of time to see the consequences of mismanaged ecologies. The Solomani, as a younger and more aggressive culture, likely are more driven by profit motives. The current Imperium is a blend of these (and others besides).
I'm hardly an expert though! This is just my guess at first pass.
So overall, no, I don't think the Imperium as a whole could make or even legally enforce any kind of Gaia initiative across all member planets. There'd also be political, cultural and regional tensions about the ideology behind such a move. Still, incentives and education could be offered to member worlds to improve sustainability and biodiversity and might well be through the Scout service and individuals (Dilettantes?) pursuing such goals privately or in the political realm.
