Better yes, but not 100%, & he was more confident with me than another rider which suggests some at least was due to trust rather than traffic proofing.
A bit of history first. William was a welshxarab who came to me as an 11yo when I was 13. He'd had one too many driving accidents & so could only be ridden, even then he was a bit edgy with large vehicles. About 3 years later we had an accident out hacking that involved us going onto a car bonnet, over the top of it & down a ditch the other side of the road, miraculously neither of us were badly hurt but mentally he was badly shaken - even parked cards in the yard car park frightened him. I was frightened my parents would see how bad things were & sell him! So I set about with a plan. He'd be fed on the edge of the car park, and once he could calmly eat his feed there I'd move it closer to a car. Slow slow inches, never moving forward until he was calm. Then me sat in a car with the door open holding his bowl. Then back off a distance & have a parked car with the engine running repeating the whole slow procedure & never advancing until he was happy. Then cars would slowly move - I'm sure by now you've got the idea lol. I was lucky so many liveries were prepared to help & in the early days not pull in or out of the car park while he was eating. We progressed to doing without the feed, then riding round the car park. Then out on quiet roads boxed in by big horses - there were times when that was "interesting" & if my parents had seen he would have been sol or banned from going on the roads! But we got there, though he had to be ridden confidently & calmly.
About 5 years later & on a different yard I was hacking with a friend when she came off and was hurt. This was before the days of mobiles so it was a case of go & get help & her horse had left the area. There were two ways to the nearest house - about 20 minutes along quiet lanes or 10 minutes but involving a stretch along a busy main road with lots of lorries. He went along that road tense but totally obedient & never a stutter, I don't think I was ever prouder of him!!!
It can be done in most cases but you have to be prepared to put in the work & also honest enough to know if some of the problem is you. If a horse is nervous it will often take confidence from a confident rider, but if the rider is also nervous then the confirm the horse's doubts & matters get worse. You can't lie to them.