Bein Hashmshos is a period of uncertainty between day and night. Shekiya is the beginning of this period when the sun sets. From this time on there is an uncertainty whether one can make kiddush yet, we therefore, wait untll after three stars are visible before making Kiddush.
According to the SA, both men and women have the same obligation to make kiddush on Shabbos and Pesach, because they are both commanded to observe these holy days. Therefore, just as one cannot drink anything before kiddush on Shabbos, the same applies on Pesach.
As double AA pointed out, can one bring in pesach early like people do for Shabbos? Can one make kiddush after plag before Tzeitz? The SA says when it is dark then one should start. The Mishna Berura and Eshel Avraham both point out that one can only start the Seder and kiddush when it is night. Therefore one can only start when it is night and can't eat or drink before kiddush.
edit
Reb Meneshe Klein here seems to be more leninat and rule if there is a need one can drink.
In short
I think one would not be allowed to drink before Kiddush. (Obviously, a Rabbi must be consulted) unless under certain circumstances.