I think there are actually very strong connections for a large number of reasons. The obvious comparison that comes to mind is grinding your own hamburger from beef your neighbor raised vs eating at Burger King.
The simple fact is that mass production generally poses sustainability problems both in terms of energy consumption and complexity costs.
I have to credit Gilbert Chesterton for this insight, but the fact is that mass production undermines localist economies and represents a sort of centralizing force that robs local communities of some of their self-sustainability. Any movement away from mass production in this regard is good.
Conversely craft cultures teach localism, re-use and repurposing of materials, and thus stand up very much against mass production of disposable goods. This also can reduce waste.
Crafts teach empowerment regarding personal production and consumption, which again is fundamentally necessary for sustainability.
I think that localism has to be a foundation of sustainability because centralization only works with complex regulation of behavior. For example the size of the US public sector today as a percentage of GDP is nearing 40%, which is historically unprecedented. The reason it is so high is because we are so productive as workers, but that productivity is subsidized by the burning of fossil fuels. Decentralized solutions are robust and cheap. Centralized ones throughout history have always achieved some economy of scale only at the expense of sustainability (they appear cheaper but in fact they only do so by utilizing surpluses from elsewhere).
This isn't a partisan attack and neither political party in the US has any credible answer to this problem as far as I can see. My point is just to highlight the relationship between surplus generated by consuming fossil fuels at an incredible rate, and the centralization both of manufacturing/distribution and of regulation and government, and the way this creates problems of sustainability. I don't think there is any serious debate about whether a very large regulatory sector poses sustainability problems (if there is, I'd like to hear it) given that such a sector must consume resources and energy and is not producing. Additionally a more robust craft movement makes it harder for government regulation to force people into unsustainable markets (say, banning sale of hand-made wooden children's toys so that we all have to buy plastic mass-produced trinkets from China), and it raises the demand for regulatory reform to cut back on laws already in place. For example more cheese-makers will make it harder to push for making it harder to purchase milk which hasn't had the proteins denatured via ultrapasteurization. (Ultrapasteurized milk won't curdle properly due to protein denaturization and chelation of calcium in the milk.) Moreover these issues are not partisan issues. They are corporatist vs craftsman issues, and the more craftsmen we have the better we are.
Nor are historical parallels far to seek. See Prof. Joseph Tainter's excellent work "The Collapse of Complex Societies"
So yes, I think crafts culture is an important piece of the puzzle. Part of the goal has to be to retain our own surpluses instead of pushing them into the machines of centralization.