This will speed the entire process. The magnesium citrate is used at the start of the elimination diet to induce bowel movements to clear the large intestine of most of it's contents. Since these contents often contain previously eaten food allergens, the overall effect it to speed 'clearing'. Magnesium glycinate, orotate or aspartate would be a much better choice. Later on, when your IBS has been resolved for a year or so, mag citrate might be a cheaper way to go.
Clearing is a multi-faceted phenomenon.
You cease to feel the intense cravings that are driven by food allergies. In my book it looks like I'm going to suggest what to eat at every meal. You will start to build a degree of resistance after eliminating food allergens. This is the whole idea behind rotation diets. Reactions tend to happen 45 minutes to 2 hours after ingestion.