You can try, but it'll be a real adventure.
First off, Reddit requires Python 2.6. This isn't available at all in any released version of Debian Linux — it is available in Debian squeeze (experimental), but our local packages are not yet available for that release at all, so I cannot recommend attempting to upgrade to it. You can probably compile and install it in your home directory, though; see http://wiki.dreamhost.com/Python for details.
The other big requirement that isn't normally available is a PostgreSQL server. You can, of course, just install one on your web PS, but if you do so it will not be managed like a MySQL PS is (in particular, we can't guarantee the availability or viability of any backups).
Everything else looks like it'll be either installed or easily installable with a PS admin account. Good luck.