Halftone effect actually converts the shape to raster image. Also blur, glow and shadow effects are raster images.
Those raster images are generated for what's shown on the screen, Illustrator still keeps the original shape (can be as well vector as raster image) hanging around. You see the effect as an insert in the Appearance panel. There you can reopen the effect dialog for readjustments or remove the effect.
Let's assume you have applied Outer Glow to a vector shape. Apply Object > Expand Appearance and Ungroup to make the generated raster image free. Then apply to it Color Halftone.
You can again expand the appearance to get the halftoned glow as a free image. Now you have got exactly what you wrote you want. But I suspect you will not be happy. It's a raster image.
You can in theory trace it back to vector but that's not practical. The image is blurry and contains transparent overlapping colors. You will not get clean dots. And the high number (thousands) of the traced new paths can slow down your system. Save at least your work before trying tracing because your system can freeze under too high load.
If you want your glow as a controllable number of vector dots something else is needed - an effect plugin or a better workflow than using Illustrators effects in a standard way with default settings.
If you can accept single color dots (much simpler that what Illustrator's color halftone generates) you can get something usable even in Illustrator. An example:
In the left there's a random vector shape. It has got Outer Glow effect. The third image is the glow raster image separated. It's got by applying Expand Appearance and Ungroup. The original shape is moved away. The rightmost image is the original shape and a half-toned vector version of the glow simply moved to the same place.
The home-made vector glow isn't perfect. You can see that it's too dense in dark areas which make waist of the shape thicker. With high zoom you could also see that the dots have irregular shapes.
But the vector glow is easy to make in Illustrator. At first draw a rectangle, place it below the separated raster glow and fill the rectangle with Illustrator's basic dot pattern:
Scale the pattern dots small enough with Object > Transform > Scale > Patterns.
Apply Gaussian Blur to the pattern (not to the glow). The radius should be set so that the dots become lighter in their midpoints, but the gaps between the dots are still visible. Zoom in to be sure. You must also have white background to see it reliably.
Select both the glow shape and the blurred pattern. Rasterize them as one item with white background and high enough resolution. 300 dpi is OK for the screen.
Apply Object > Live Trace to get it as B&W vector. It's a good idea to place the original vector shape on the top to see how tracing settings affect to the glow effect:
The outlines and high zoom in show how well or badly it succeeded:
The round dots are not optimal. Somehow better result is possible if one copies the glow shape to Photoshop, converts it to grayscale and bitmap color mode. Photoshop has several bitmap halftoning options which do not make the dark are too dense, the waist of the shape stays as narrow as it originally was. This is Diffusion dither half-toning:
Converted from bitmap mode to RGB, pasted back to illustrator, traced and layered with the original shape the result is this:
As seen from far away it looks like the blur based glow and it is vector, but unfortunately it has much more paths and nodes than the dot pattern based version.
Photoshop's Halftone Screen half-toning in the bitmap color mode gives also good results which as vectorized are a little lighter. But the dots are like crosses. 0,5 pixel blur in tracing reduces the number of paths substantially by removing the smallest dots:
I stop here. There's many possibilities still available. If it happens that you are in a hurry and not interested in tinkering, do as user Scott suggested; get a plugin for vectorized half toning patterns.
