Hi Eric
Yes, this should be possible, there are two ways I can think of doing it. Have you considered putting all the sites into a related table (repeat) so that you can create a new record for each site, which they can have their own details and own geopoint question.
Otherwise you could use the null esri field type against the additional geopoint questions, and use a calculation to pull the lat/long into text fields and store the values.
Phil.