Hi Shawn,
To summarize your situation, you want to join a polyline created from calling ConstructGeodeticLineFromPoints (polyline_1) with an existing polyline, say polyline_2, right? If that's the case, you can use ISegmentCollection like this:
Dim pSegColl_2 As ISegmentCollection
Set pSegColl_2 = polyline_2
Dim pSegColl_1 As ISegmentCollection
Set pSegColl_1 = polyline_1
pSegColl_2.AddSegmentCollection pSegColl_1