John, absentee precinct results can't be reported by district in VTS but can in GEMS.
In order to report correct absentee results by district, absentee precincts must be defined so as to coincide with the Congressional district boundaries. That is, the base precincts that comprise each absentee precinct must coincide one-to-one with the base precincts comprising the corresponding district. If the absentee precincts do not follow district boundaries, absentee results reported for a particular district will include the total results of all absentee precincts that comprise any base precinct in the district in question, which would give you potentially incorrect results.
Remember that the summary report allows you to report all results, polling and absentee, on a summarized basis, so that it is not necessary to just view absentee results with the Congressional breakdown. However, in the SOVC, including absentee results will then necessarily mean reporting by Congressional district, and it will not be possible to report absentee results both Congressionally and by some other district in the same election.