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Yes, you can define the Michigan GeoRef coordinate system in MapViewer 7 and Didger 4 and use it as the original coordinate system of imported files, or as the destination coordinate system when performing a projection conversion.

The information below was obtained from the Michigan Department of Natural Resources (PDF attached, pages 3 and 4) and by finding some information on the internet, such as on the ESRI site (http://support.esri.com/index.cfm?fa=knowledgebase.techarticles.articleShow&d=15231).

Michigan GeoRef uses a form of the Hotine Oblique Mercator projection. You can define the Hotine Oblique Mercator projection either by specifying 2 points on the central line, or by specifying 1 point on the central line and an azimuth. Didger 4 only allows you to use the 2-point method (despite what may be read in the Help). MapViewer 7 lets you choose between the 2-point method or the 1-point+azimuth method.

The projection, projection settings, and datum to use are as follows:

Projection System:
Hotine Oblique Mercator

Projection Settings (1-point+azimuth method):
Central Scale Factor: 0.9996
Central Longitude: -86.000
Central Latitude: 45.30916666666667
Azimuth: 337.25556
False Easting: 2546731.496
False Northing: -4354009.816
Ellipsoid (MapViewer): GRS 1980

Projection Settings (2-point method):
Central Scale Factor: 0.9996
Central Latitude (Didger): 45.30916666666667
Longitude of 1st Point: 0
Latitude of 1st Point: 0
Longitude of 2nd Point: -91.88228
Latitude of 2nd Point: 40.40157
False Easting: 2546731.496
False Northing: -4354009.816
Ellipsoid (MapViewer): GRS 1980

Datum:
North American Datum 1983