Is it okay to use something like Movable Type, Greymatter, or B2 to maintain a journal/blog?
It certainly is fine to use such software on your hosting account. We also have all of the “extra” PERL modules installed and available for using Movable Type. We do though recommend against Greymatter for larger journals, as the rebuild time could potentially stress the webserver. We haven’t had a problem thus far with anyone using Greymatter but on larger sites it may take up to twenty minutes to rebuild or perhaps longer. B2/Cafelog would be strongly recommended in this case as there is no rebuilding necessary.