AFAIK, you have transparency in a PGraphics only in JAVA2D mode (at least it doesn't work with P2D -- just tested, works fine and fast in P3D). Which is unfortunate as the JAVA2D way of running your sketch is much slower. Probably because you use point(), which is slow.
About the green flash: for some reason, background() acts immediately on the screen (while other drawings wait for completion of draw()). If you move the call just before the image() call, you don't see the green flash (but instead see the default gray background...
).
If you use pixels array instead of point(), you have a more reactive sketch:
Code:void draw () {
PGraphics test = createGraphics(width, height, JAVA2D);
test.loadPixels();
for (int x=0; x < width; ++x) {
for (int y=0; y < height; ++y) {
color c = color(255, 0, 0, noise(x/100f,y/100f)*255);
test.pixels[x + y * width] = c;
}
}
test.updatePixels();
background(0,255,0);
image(test,0,0);
}