SIDs use wavelet compression, which is not a supported compression type that ArcGIS can write to. JPEG 2000 compression, which is a supported compression type, uses wavelet technology to compress rasters, however if you want to achieve a lossless compression, you cannot use this method within a file geodatabase or ArcSDE geodatabase. For file geodatabases and ArcSDE geodatabases, you would want to use LZ77. See the following link for more information.
I've also attached a PPT for a presentation I had to give comparing the storage of a raster dataset vs a mosaic dataset. The source data is 130 SID images that are each 3.5 MBs on disk (66 MBs uncompressed). The PPT demonstrates the time and storage saved using a mosaic dataset rather than a raster dataset. Note: raster dataset is stored with LZ77 compression.
Also, here are some screen shots comparing the raster dataset and mosaic dataset using the PerfQAnalyzer (same data, but the raster and mosaic dataset both reside in a File Geodatabase).
Raster Dataset:
Mosaic Dataset:
You can see the mosaic dataset renders faster (performed 3 zooms for each dataset).