It might be possible to somehow convert at least partial data between BSQ and ADF formats with some programs from ESRI like ArcView. Howerver no relevant information bout this subject could be found.
Convert ArcView band sequential image file to ArcView ARC/INFO coverage data.
We found one software available in the database for this conversion.
Microsoft Windows software - convert bsq to adf on Windows
A GIS application used to work with geographic data
Convert from bsq file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.