Is there any way to check if an element has jquery select2 already applied to it?

you can check if the element has select2 attribute

$('.MyDripdowns').each(function (i, obj) {
    if (!$(obj).data('select2'))
    {
        $(obj).select2({ width: "455px" });
    }
});

EDIT

As @Fr0zenFyr said in his comment for v4.0 you can use :

if (!$(obj).hasClass("select2-hidden-accessible"))