You should be able to render the same brush stroke many times pixels apart to get the effect you want. If you jitter the renders with a Gaussian distribution you will get a Gaussian blur.
This would be similar to jitter antialiasing with an accumulation buffer, but instead of using subpixel offsets you would use multi-pixel offsets as big as you want the blur effect. You'd would want to probably render around 16 times to make it look smooth. http://www.opengl.org/resources/code/samples/advanced/advanced97/notes/node63.html
This is also similar(or really the same thing) as jittering to create motion blur. http://glprogramming.com/red/chapter10.html
You wouldn't even NEED to use a separate accumulation buffer here, just render each pass with alpha that adds up to solid. One thing to remember, you want to always jitter across the same offsets so that successive frames look the same(i.e. if you are using random offsets then every frame will have slightly different blur effect).