Depends on the airline. On Aer Lingus this would work no problem. On KLM, it wouldn't.

On KLM, if you miss a segment, all remaning segments will be cancelled, unless you have the airline intervene and "protect" the remainder of your reservation. This could occur, for instance, if you made contact with the airline before the missed segment, or immediately after check in has closed/departure, provided you can provide a satisfactory explanation for having missed the flight and the agent you speak to being sympathetic.