Of course you could put Steam on there. Ideally you would install your OS and all your applications to the SSD while storing bulk data on the hard drives, but for games, that might not be entirely practical yet from a cost perspective if you have a large library that you want to keep installed, and don't want to spend money on a huge SSD.
You can set up multiple game install folders on different drives from within the Steam client though, allowing you to install your most played games to the SSD, while keeping others on the hard drive. From in Steam, go to "Settings > Downloads > Steam Library Folders > Add Library Folder" to add an install directory on another drive. Then, when installing a game, pick your desired drive from the "Choose Location For Install" box. Or, if you already have the game installed on one drive, and want to move it to another, you can right-click the game in your library, and choose "Properties > Local Files > Move Install Folder" to move the game from one drive to another. Just keep in mind that it might take some minutes to complete the transfer process, depending on the performance of the slowest drive, and how large the game is.