SUBSTRING performance for large BYTEA

I'm working on reading large BYTEA fields from PostgreSQL 8.1. (For
legacy reasons, it's unattractive to move them to large objects.) I'm
using JDBC, and as various people have pointed out
<http://archives.postgresql.org/pgsql-jdbc/2005-06/msg00138.php>, the
standard stream-style access method runs out of memory for large BYTEAs.

Karsten Hilbert mentions using SUBSTRING to read these BYTEA fields a
chunk at a time
<http://archives.postgresql.org/pgsql-general/2005-01/msg00032.php>.
I've tried this, and indeed it works. (Once I corrected for the 1-based
indexing ;-))

My question is about performance in the postgres server. When I execute
"SELECT SUBSTRING (my_bytea FROM ? FOR ?) FROM my_table WHERE id = ?",
does it fetch the whole BYTEA into memory? Or does it access only the
pages that contain the requested substring?

Vance