There are two stages in the work of MobileJoomla:
1) Pre-stage: type of device is detected, and template is changed to mobile ones if necessary (it's possible to don't change template at all, e.g. if you have good responsive template), some modules and plugins may be disabled, and homepage may be changed to "mobile" one.
2) Post-stage: rescaling of large images, removing unsupported tags (e.g. flash banners, etc.).
So, website content is the same, an "envelope" (template and set of modules) may be changed only.
Joomla!1.5 is supported (I don't remember exact minimal required version, should be something like 1.5.20).