No. Even though, Snappy is Ubuntu and completely compatible with other Ubuntu installs you will not be able to install and run pre-packaged applications.
Snappy introduces transactional updates and moves away from the repository paradigm. Meaning there are very few packages out there for Snappy currently, given its short existence. It also sports a read-only file-system in two partitions in order to be able to do quick roll-backs.
That is also the only difference between Ubuntu Server and Snappy. Snappy is really only a way to update and/or extend your system, it fills the function of apt-get. Here's Mark's explanation as to what Snappy really is. However, Snappy is mostly released and marketed in connection with Ubuntu Core as a base OS. When you download images referring to Snappy, it will be with Ubuntu Core as a base.
Ubuntu Core is a minimalist Ubuntu installation. It existed before and without Snappy, but it seems that Ubuntu Core and Snappy are
becoming the same thing. The Ubuntu Core website is now a link to
Snappy. Anyways, here's some basic info
In addition, the arm architecture has even fewer alternatives as of right now (I'm assuming this is relevant to you, if you're going to run it on SBC). On my armhf based install (on a beaglebone) there are currently around 20 different applications available for install. However that is a 15.04 beta install. I am unsure if you are able to install Snappy on older stable Ubuntu Core installs, and whether that will give you more options.
Canonical's Dustin Kirkland has a great write-up about what use-cases Snappy Ubuntu covers here.