Not usually. OwnCloud requires server setup, special access permissions, and configurations that are not well supported or easy to achieve on shared hosting plans. Moreover, shared hosting Terms of Service usually indicate that customer plans are intended for website publishing, not file storage. Even if you can get ownCloud setup and configured, you may fall afoul of your user agreement.
If you want to setup ownCloud on a hosting plan, you will have a much better experience using a VPS plan.
