Technically you could solve this in two ways: There is nothing preventing you from connecting to the same database with two OpenERP Instances. So you can make two installations and allow one to be the ERP frontend and the other one to be the store.

You could sync the database and use a copy of the database on the webserver.

So far I believe the Store is too tightly embedded and can't be separated right now, you could try and install base openerp and base web module but I bet it will fail as most modules will not be available. This is something I have not yet tried.