take it from someone who has done this 9 of sorts) It is worth it. It’s unlikely to cost much if the fundamental parts are sound. However it may take some time. This however wouldn’t be for a full restore, as it may be a money pit if you want everything like new.
ie. – you prolly do not need to replace the headset. Clean old one and get £2 of bearings from a supplier. Tyres – search ebay etc, look for clearance deals on parts. Cranks can prolly be polished with some effort etc. Surely a fixie is only going to get grimmy and work on the roads anyway. Why make it perfect? I thought was the whole idea of them anyway.
It may be time consuming as that last wheel nut may take 2 hours to loosen, those wheel bearings need to be sourced, that cotterpin needs replacing etc.. but that’s all part of the fun and satisfaction at the end.
I would just make it functional and look presentable. Wouldn’t bother with a full restoration personally.
Good luck. When it works you’ll love it.