With the help of dynamic fields it is easy to implement the opposite procedure - displaying the current height (Z-coordinate) of a block into the value of one of its attributes.
However, if you have a drawing with blocks (e.g. survey points) coming from an external source, all lying in a plane (Z=0), and you need to move these blocks to the actual elevations specified by a numeric value in one of their attributes, you can use the freeware LISP utility Att2elev.
Download the application from Download, load it into AutoCAD with the APPLOAD command and invoke it by typing the command ATT2ELEV.
Then select a specific attribute that contains the elevation data. If its numeric value is preceded by a prefix or ends with a suffix (e.g. "123.4m"), you can specify the extra text ("m") to ignore it when determining the elevation. Then by selecting the block references or by confirming "all", the blocks of the same type will be moved to the heights specified by the values of these attributes.
Note: Autodesk Civil 3D already includes a built-in feature for this type of operation