I'm importing several gigantic csv files into a table - so I'm wondering what would happen if I ran COPY FROM jobs concurrently?
It just works, like it should. It doesn't lock the table, so start testing.
If you're trying to speed things up, this is generally a good idea. I say "generally" because you can also speed things up by creating the table and loading data into in a single transaction, which reduces transaction logging. You'd have to test to see which is faster.
In PostgreSQL versions prior to 9.2 (currently in beta), the maximum number of concurrent beneficial COPYs tends to be 3. In 9.2 that goes up to at least 8, assuming you have the cores and I/O available.