My family has a custom to read the hagadda on the Shabbos before Pesach, from עבדים היינו until לכפר על עוונותינו. This custom is mentioned in many hagaddos, and in the Ezras Torah Luach (although that last mentions that the Gra opposed this custom).
Double AA pointed me to the Rema (OC 430), who mentions this custom. I skimmed the nos'ei keilim on the page, but didn't see that anyone explained the reasoning behind the custom. The Gra there explains that this custom should not be followed because the hagadda should be reserved for the "שעה שיש מצה ומרור מונחים לפניך," the time when you have matzah and maror on the table, meaning the seder. (Based on Mechilta, at the end of Bo.)
None of the above sources mention why the hagadda should be read. I suspect that it is so that a person can familiarize themselves with the text ahead of the seder (my father shares this suspicion), but I'm looking for a source that explicitly explains the reasoning for this practice.
I checked the ספר טעמי המנהגים, which supplied reasons for calling the day "Shabbos Hagadol," the haftorah, and the Shabbos Hagadol derasha. None of the hagaddos I've seen explain the custom, but I will continue searching.