Don't quote the regex when specifying a regex in js. Forward slash is enough.
alert($('#datepicker').val());
if($('#datepicker').val().match(
/(\d{4})-(\d{2})-(\d{2})T(\d{2})\:(\d{2})\:(\d{2})[+-](\d{2})\:(\d{2})/
)) {
alert('ok');
} else {
alert('not ok');
}