Almost anything is doable

We'll just have to revert to my idea of using a cookie.
1) Set up the array filter exclusion between Q1 (the checkbox question) and Q2 (the radio question).
2) Add the following to the end of your template.js file. It is a little script to allow the recovery of cookies.
// a function to get the value of a cookie by name
function getCookie ( cookieName ) {
var results = document.cookie.match ( '(^|;) ?' + cookieName + '=([^;]*)(;|$)' );
if ( results ) {
return ( unescape ( results[2] ) );
}
else {
return null;
}
}
3) Add the following to the source of Q1. Replace "3" in line 24 with the minimum number of options you would like to display in Q2. The script interrupts the next/submit function, does some math and if less than the minimum number of options are to be shown sets a cookie with a value of 1.
<script type="text/javascript" charset="utf-8">
$(document).ready(function() {
function minShown(minAllowed) {
// Interrupt next/submit function
$('form#limesurvey').submit(function(){
var visible = $('.multiple-opt input.checkbox').length - $('.multiple-opt input.checkbox:checked').length;
// If less than the minimum, clear the question and move on
if(visible < minAllowed) {
document.cookie = 'lsSkipQ = 1';
}
else {
document.cookie = 'lsSkipQ = 0';
}
// Carry on with submit
return true;
});
}
minShown(3);
});
</script>
4) Add the following to the source of Q2. The script retrieves the cookie and if the value is 1, unchecks all radio options and moves to the next question.
<script type="text/javascript" charset="utf-8">
$(document).ready(function() {
// Retrieve the cookie
var skip = getCookie ('lsSkipQ');
// If we're supposed to skip, uncheck all options and move on
if(skip > 0) {
$('.list-radio').hide();
$('.list-radio input,radio').attr('checked', false);
document.limesurvey.move.value = 'movenext';
document.limesurvey.submit();
}
});
</script>
5) Add the following to the source of Q3 (the next question after the skip). The script retrieves the cookie and if the value is 1, adjusts the "Previous" buttons action to skip over the Q2 and go directly back to Q1.
<script type="text/javascript" charset="utf-8">
$(document).ready(function() {
// Retrieve the cookie
var skip = getCookie ('lsSkipQ');
// Skip previous question
if(skip > 0) {
$('#moveprevbtn').mousedown(function () {
$('#thisstep').val($('#thisstep').val() - 1);
});
}
});
</script>