I would suggest that no, you don't need sunscreen because 0.2-0.4 is an extremely low UV index. You can't really go lower before nightfall!
However, the UV index only measures UVB, so many not be a good guide for UVA levels. UVA causes pigmentation and wrinkles but not burning.
I do want to correct the myth that UVA does not vary across the year or by latitude. Neither is true and I'm not sure how these illogical rumours have gotten such a foothold. There is about 3 x as much UVA in Summer as in Winter. UVB varies by a factor of about 6 from Summer to Winter. Also in Summer in Northern and Southern latitudes there are more hours per day of potential UVA exposure, compared with the short days of Winter.
And total annual UVA does vary a lot with latitude, which is why the human race has varied skin colours that correlate with latitude of origin.
Edited by StephCThomp, 08 December 2014 - 10:40 AM.