At the recent BALPA Employment Opportunities Conference a couple of airlines did express a preference for Integrated students. However, these airlines were hardly recruiting anyone over the next year e.g. six FOs. So it was no factor on the grand scheme of things.
I think the problem with doing a PPL in a short time out in the US is trying to grasp the fundamentals of the ground school and learn to fly the aircraft is quite demanding. You may get the ticks in the boxes but thoroughly understanding everything is another matter (I did mine in the US). Most people in the UK doing PPLs will do it over many weekends and thus have plenty of time to absorb all the new information they are learning.
Biscuit