Normally, when not flying a leg in your reservation, the airlines will cancel the rest of the reservation. Does the same rule apply for open-jaw reservations? I can't seem to find any official reference for this.
If it's the same airline the whole way through and/or all sectors are on the one ticket, it will be counted as a 'no-show', and your onward flights will most likely be cancelled. If it's a separate airline and a separate ticket, then the no-show prior to the ARNK shouldn't impact your onward travel.