Depends, how bright are your streets?
No, because Tri-X looks so good in Diafine at 1250-1600 I don't bother. I stock Tri-X as my standard 35mm 400 film. I also keep TMZ on hand and for street photography at night, something I don't do much but do occasionally, I'll use that at 3200 or even 6400. But I shot photos at a street arts festival recently when I was out of TMZ and I used the Tri-X/Diafine combo and got some good shots. In some cases shutter speeds were really straining the limits of hand holding with my f/1.7 50mm lens, but I do have some good ones.
I've also seen good results from others pushing HP5+ to 1600.