Yes. To have multiple galleires on the same page you will need to attach all of the images to the page first, and then use shortcodes to designate which images you want included in each gallery. http://support.wordpress.com/images/gallery/#gallery-shortcode.
After you upload the images go to to Media > Library, hover over each image name, you take note its ID number at the end of the information displayed in the status/progress bar of your browser, then you go to the page editor, switch to the HTML editor, and use the gallery shortcode image ID number for the images you want to include.
Or you upload the one group of images via the post, upload the rest via a page you’ll create for the purpose, get the ID of the page and use it with the gallery shortcode. This way you’ll only need one ID number instead of many.
But you’ll need to replace the regular top menu of the theme with a custom one, so that the dummy pages won’t show up.