If you are using a version prior to 3.0 you will need to update to the latest version of Parallax to be able to do so.
Updating your theme is free and instructions are here.
The short answer is YES!
As can be seen in this live example you can position a Slideshow at the top of your homepage.
( Online Store > Themes > Customize > Add section > Slideshow > drag that Slideshow section to the top of the Section tabs )
Once you're updated, feel free to check out our Parallax homepage setup video.
Versions prior to 3.0 of the Parallax theme do not support having a rotating slideshow.
You may want to review this blog post for some suggestions on how to design full width banners.
If having a slideshow on the homepage is essential, and you do not wish to update you may want to consider our Retina theme as it has many of the same design characteristics as Parallax and allows for a slideshow on the homepage.
You may be able to add custom code to change the first banner image in Parallax to a slideshow, however, this is considered a customization and is outside the scope of what we can support. You may be able to have a Shopify Expert help out (though see this post about the downfalls of customizing your theme).