I think it's possible. The following way is only the 1st idea I have, not necessary the best one.
The plugin created in your blog a page called Newsletter. Its slug should be newsletter.
So in your theme folder you can create a new file called page-newsletter.php (you can duplicate the standard page.php and edit it).
In this new file you should simplify the header and probably remove sidebars, menu ecc. But be sure to leave the
Using this way, please note that the newsletter page will be always shown using the customised theme file you created, also when it is called not in modal. To solve it you can append a query var in the link that calls the page: so in the top of page theme file, you check if this var exists (and load the part of the file that shows modal version) or not (and load the part of the file that shows normal version).
I hope to be understandable, sorry for my bad English...