Currently not. You cannot set an array of n fields in you WP_Customize_Manager::add_control method in the customize_register action hook.
The class creating the controls is WP_Customize_Control and does only accept the following types:
- checkbox
- radio
- select
- textarea
- dropdown-pages
- and per default any valid input type
You will need an options page to edit/create your gallery data with thickbox (media gallery) integration.
A posible workaround
Create your own class extending WP_Customize_Control and overwrite the relevant methods. There create controls to handle the array of gallery images and thickbox integration. Finally follow the path of the Custom Theme API and you are set to go.