A starkit is as platform independent as the application code it contains.
What this means, is that if the application consists of pure Tcl/Tk scripts, and if GUI issues have been dealt with (font differences, etc), then a starkit can be used on over a dozen different platforms, by simply running it with the appropriate version of Tclkit.
If the application does platform-specific things, such as running exec and relying on specific programs or using specific OS/GUI features, then evidently starkits will not necessarily run everywhere. The good news is that many platforms dependencies can be avoid or resolved with Tcl.
If the application relies on compiled extensions, stored as shared libraries inside the starkit, then it will only work with the platforms for which compiled extensions have been supplied, unless the code is written in such a way that it falls back to a platform-independent approach if a shared library is not available.
The file format of starkits is based on the Metakit database package, and is essentially portable and usable on all platforms, from 16- to 64-bit, and both little- and big-endian. That includes binary data stored with Metakit.