Yes, you can do that by selecting the points with the Digitizer Tool, then right clicking and selecting the option to apply elevations from the loaded terrain data.
I would suggest perhaps the NED data (assuming you are in the US) available from the File->Download Online Imagery/Data menu command, or you might go to
<i>The National Map</i> Seamless Server and pull down the even higher resolution (1/3 arc second or about 10 meter resolution) NED data and load that.
Let me know if I can be of further assistance.
Thanks,
Mike
Global Mapper Support
support@globalmapper.com