i think it is possible,
but i also think that you need to create your own shortcode-plugin. because gallery is a array;
and because you use repeater it will became even more difficult than without. because you have a array(gallery) inside a array(repeater). but it should still be possible.
for easier work you may need an additional field for each gallery that is used as identifier for your shortcode.
you can work with get_field/get_sub_field inside your shortcode plugin if you do it correct.
easier way would maybe be:
work with flexible content field, that contains a wysiwyg and a gallery layout, and create a frontend layout for it.
