Hello,
ENVI version 5.1 has a Seamless Mosaic workflow that is simple to use. Plus ENVI uses the Esri projection engine, which means that nearly all of the projections available in ArcMap are available for use in ENVI. So your georeferencing details from ArcMap should be retained when using ENVI. Here are some tutorials that describe the Seamless Mosaic workflow:
Simple workflow (for quickly creating a georeferenced mosaic):
http://www.exelisvis.com/docs/mosaict...
Advanced workflow (color balancing, seamlines, etc.):
http://www.exelisvis.com/docs/mosaica...