Didn't know that - I just tried on one existing table and it failed on account of index row too short
ERROR: index row requires 14616 bytes, maximum size is 8191 SQL state: 54000
Although it looked suspicious like it could be solved by defining custom tablespace (never did that on Postgres so I am not sure if it would work), I assumed that it is because bytea can't be indexed.
Your conclusion is not entirely correct; the problem is that each value in an index is limited to 8191 bytes. Your bytea value is longer than that and therefore the value can't be fit into an index entry. Hence the error.
People usually work around that, for example by defining a functional index on only the first 8191 bytes.
I haven't personally done that with bytea columns, but I think it's safe to assume that is possible.
-- If you can't see the forest for the trees, Cut the trees and you'll see there is no forest.
