Is the prayer of one who قطع صلاته جالساً due to a headache and a desire to vomit valid?

It is forbidden to interrupt a fard (obligatory) prayer without a valid excuse. It is obligatory to complete it, even if you have to motion for prostration while sitting. If you pray the fard prayer sitting while you are able to stand, your prayer is invalid, and you must repeat it immediately. Every possible pillar of the prayer, such as standing and bowing, must be performed; only what you are unable to do is waived.