Headset Bollocksed

Hello all, been a long time since I've been here and nice to be back.

I'm slumming in Spain at the moment and I've just bought a geared rustbucket to ride around. It was very cheap, so I was expecting problems, and having trued the wheels I have now discovered the first biggie - the headset is really, really stiff when you turn it left.

TBH, this doesn't make a lot of difference to the handling of a cheap 1000 year old bike that is too small for me anyway, but for some reason I find it annoying. According to Park Tools:

Very worn headsets tend to "lock up" when the front wheel is pointing straight. Pick up the front of the bike, and gently swing the handlebars back and forth from center. Pitting in the cups will cause the headset to stick as it passes through center position. A pitted headset should be replaced. New headsets are pressed into the frame and fork.
This is what has happened, right?

Once I've found somewhere to stay and a way of earning money, I'll do something about it. How likely is it that the bike will turn into shrapnel at a busy traffic junction in the meanwhile? Bear in mind that the roads here are pretty straight, so I don't need to do much steering, and I can't get the thing going faster than about jogging pace anyway.