It is possible to run Limesurvey without root access, a lot of people do so. As long as you have FTP access, can create a database and the server runs the right version of PHP, you should be good. You can also install plugins, themes (question, survey, admin), etc.
There are people out there who run Limesurvey even on shared webspace. Of course, this is nothing for big surveys, but if you have a survey with a couple of responses, this works as well, as long as the survey isn't to heavy and the shared webspace isn't too shabby.
Caveats:
You probably can't adapt configurations for PHP, etc. Depending on the configuration of your server and your needs in terms of surveys, the default settings in php might not be enough (e.g. max_vars, max_executiontime, etc). But if it is a managed server, you either have a admin page to adapt this (Cpanel, Plesk, etc.) or the person who manages the server for you can set this when needed.
Help us to help you!
- Provide your LS version and where it is installed (own server, uni/employer, SaaS hosting, etc.).
- Always provide a LSS file (not LSQ or LSG).
Note: I answer at this forum in my spare time, I'm not a LimeSurvey GmbH employee.