Yes. You can point towards a shared theme CSS file from within each gallery's embedding code using the themeUrl option (noted in the Embed Options section of the Config Options page).
The themeUrl value can be an absolute URL (starting with http:// or https://) or a relative path (relative to the web page containing the gallery's embedding code).
For example:

<!--START JUICEBOX EMBED-->
<script src="jbcore/juicebox.js"></script>
<script>
    new juicebox({
        containerId: "juicebox-container",
        galleryWidth: "100%",
        galleryHeight: "100%",
        backgroundColor: "#222222",
        themeUrl: "my_themes/custom_theme/theme.css"
    });
</script>
<div id="juicebox-container"></div>
<!--END JUICEBOX EMBED-->

If you edit a gallery using JuiceboxBuilder-Pro, then the only thing you need to update on your web server is the gallery's 'config.xml' file (which holds the gallery's configuration options and image data). (You'll also need to update the 'images' and 'thumbs' folders if you add any new images, though.)
There is no need to update the gallery's embedding code (unless you change the gallery's background color or dimensions) so you can leave this in place on your web server with no need to overwrite it with a version that does not contain the themeUrl.

If you use the gallery's own 'index.html' page (generated by JuiceboxBuilder-Pro) to display the gallery on its own web page (rather than embedding the gallery in an existing web page alongside other content) and are in the habit of uploading the entire gallery folder to your web server after editing, then you can modify the template file that JuiceboxBuilder-Pro uses to generate the 'index.html' page so that the themeUrl is present in every gallery you create and edit.

Open the following file in a plain text editor and add the themeUrl to the embedding code:
Windows: C:\Program Files (x86)\JuiceboxBuilder-Pro\template\index.html
Mac: /Applications/JuiceboxBuilder-Pro.app/Contents/Resources/template/index.html

For example:

<!--START JUICEBOX EMBED-->
<script src="jbcore/juicebox.js"></script>
<script>
    new juicebox({
        containerId: 'juicebox-container',
        galleryWidth: '%%WIDTH%%',
        galleryHeight: '%%HEIGHT%%',
        backgroundColor: '%%COLOR%%',
        themeUrl: '/my_themes/custom_theme/theme.css'
    });
</script>
<div id="juicebox-container"></div>
<!--END JUICEBOX EMBED-->

The leading slash in the themeUrl above denotes your root directory (i.e. the themeUrl is a relative path always starting at your root directory) so such a themeUrl would work in any page throughout your website without modification.

Great! Just give me a shout if you run into any problems and I'll try to help you out.

You'll likely need to run whatever editing program you use as an administrator (as well as being logged  on as an administrator).
Rather than just double-clicking your editing program's shortcut, right-click it and select 'Run as administrator'.

Incidentally, after opening your editing program via 'Run as administrator' you may not be able to drag and drop the 'index.html' file into the program. You may need to use the program's 'File -> Open' functionality to open the 'index.html' file instead.

I hope this helps.