Tom Anderson wrote:

We had a very brief argument about this a month or so ago; Barry Salter
said they did, i said they didn't, and Clive threatened to excavate as
much of north London as was necessary to find out.

This is not an authoritative answer, but i did finally notice that
according to Quail, they do cross, and the crossing is indeed a little way
south of Harringay Green Lanes; probably too far to build a station with
interchange, though.

This crossing is also shown on the Quail London Transport Railway Track
Map (fifth edition, 1995) - just to the north of Manor House station.
This map only covers Underground and Docklands lines, so Harringay Green
Lanes is not shown on it.

--
John Ray