If I update a row, is it possible to chunk the data into the bytea column in several small steps?
Yes, it's possible. But it's a horrible idea. PostgreSQL, and all MVCC databases, writes a new row with every update so on the last chunk you'll be writing 200 MB not 1 MB.
You may consider large_objects to get around this, or better yet not using a database for this because databases are not file systems, and instead just using an IO buffer or the file system write cache. If you need to link that to data in a database, try a
path. That's what they're there for (internally the file system uses inodes). Check out btrfs or zfs if you want the PostgreSQL of file systems.
PostgreSQL is the best tool for the job if you're doing the right job, but it's not the best tool for any job.