Yes, it is possible. It is, however, of low value to do so.
.mat files are just files, so they can be read in as arrays of uint8, and those arrays of uint8 can be stored as blobs in a database.
However, all you can do with those blobs is ask about things like the length of the blob, or retrieve the blob in case you wanted to do something like compress the blob as part of a corpus of tests on how well various compression routines do.
To go beyond that, to examine the contents of the .mat that you had stored, you would need information about the detailed binary structure of .mat files. That is documented for MAT5.0 format, but is not completely documented for MAT7.0 files. For MAT7.3 files, all that is documented is that it is a modified HDF5 format.
It is possible to retrieve a blob from the database, write it out to a temporary file, and then use the usual facilities such as load() to retrieve information from the temporary file that was saved from the blob. Many people would suggest that if you were going to do that, then you might as well just store the original files.
Some various recommendations on what you have to tell Microsoft Access in order to store BLOB: