I don't see that happening for significant amounts of people. Nobody in Western Europe has to worry about necessities (for a reasonable definition of necessities, if it includes vacations and cars, then this isn't so), yet we don't see the unemployed get super productive and use their free time and energy. Instead, we usually see them degenerate, watch TV all day and slowly wither away. At the same time, it's people with jobs who make the extra time to volunteer and do things.