Yes shared hosting packages also offer e-commerce website hosting services. You can install your e-commerce from your cpanel itself.... ie from cpanel >> Software/Services >> Fantastico or Softaculous any one of these which is present on your server.
Off course, you can host your Magento based shopping cart on shared hosting as well. However, first you need to check few more details about system requirements for Magento hosting. You should consider below URLs for more information.
Our Shared hosting packages includes everything you need for an e-commerce website. With cPanel on linux web hosting package and DotnetPanel on windows hosting, one can easily install e-commerce script from the control panel itself.
However, all it depends on what type of e-commerce cart you want to pick. Few shopping carts demands more resources such as Magento.......and if it's not set up properly and professionally on the powerful server, then certainly it can be slow down the performance.