If your training the integrated route,and one of the FTO's take you on with any conviction (unlikely), then you'll be trained in approx 2 years which will be nearlly 4 years since your conviction. This means when employable your conviction will show up on a disclosure and slim chances of landing a first job, as you say why you when there's a non-convicted pilot..
But if you train the modular way and take your time with the training, when you become employable your conviction is spent and will not show up on a disclosure aslong as it over 5 years since convicted.Not completely dishonest as in the eyes of the law it is classed as spent and your legally obliged to omit it from applications.
I was in the same situation as you a few years ago and after lots of consideration took the latter option. CTC told me although they liked my honesty there is no market for a pilot with a alcohol based conviction, not when there's another 1000 pilots without. Hope it helps.