Hi Jennifer,
You can accomplish this by doing the following in AutoCAD, you can also set this up as apart of an AutoCAD template file so you'll only have to do this once if your CAD users then start to draw with that template.
1. Add a feature layer to your drawing, needs to be a point feature layer in order to assign a block.
2. Create a block or edit an existing autocad block to include a block attribute. If this block attribute has the same "tag" name as a field name in the schema of that feature layer, ArcGIS for AutoCAD will automatically link the two up. You can add more than one block tag on a single block.
2a. Click here to see the help doc on how to make an AutoCAD block attribute
3. After saving your new block use the "Assign symbol" tool from the table of contents on the point feature layer in ArcGIS for AutoCAD
3a. Click here for the Assign Symbol help doc
3b. If you want to set this up before hand so this is all done automatically, you can name the block the same as the autocad layer where the point web feature layer is drawn. For example if you have a point feature layer name "Meters" it will draw on the AutoCAD layer "ESRI_Meters". Name your block "ESRI_Meters" to make the apply symbol logic happen without having to set it from the TOC.
4. synchronize your layer in order to redraw the points as blocks.
Now that this is done. Your points from that feature layer with be symbolized as blocks with block attributes that display GIS attributes. Your CAD users can then just edit the blocks attributes to update the GIS attributes.