A UBI combined with an income at even NMW would greatly increase quality of life and hence productivity, with a much higher motivation to work.
You've definitely got a lot of faith in the public, I don't believe long term it'll have any real effect to increased productivity levels. If anything I suspect it'll have a negative effect as more people decide to give up work.
You'll either have a portion of people who will happily just live off a UBI lifestyle, or you'll have a large proportion of say millennials who will work long enough to pay off things like a mortgage, and then retire from work in their 50s because a UBI lifestyle at that point is more than affordable after your biggest expenditure is taken care of.