See [Building a custom tclsh] for a usage example. Tcl_init is documented on the [library] man page, where it says:
''To access the procedures in the Tcl library, an application should source the file init.tcl in the library, for example with the Tcl command''

 source [file join [info library] init.tcl]

''If the library procedure Tcl_Init is invoked from an application's Tcl_AppInit procedure, this happens automatically. The code in init.tcl will define the unknown procedure and arrange for the other procedures to be loaded on-demand using the auto-load mechanism defined below.''
----
[Donald Porter] wrote in [the comp.lang.tcl newsgroup]:

Bob Techentin  <techentin.robert@mayo.edu> wrote:
''Correct me if I'm wrong, Jeff, but you still need to have a Tcl script library for your application to function.  You may not need a Tcl installation on systems which will run this program with an embedded interpreter, but you must have TCL_LIBRARY pointing to a directory with at least init.tcl.''

It really depends on what the application is expecting from its
embedded Tcl library.

Tcl_CreateInterp() creates a fully functional Tcl interpreter.
All that Tcl_Init() adds (by finding and evaluating the installed
init.tclfile ) is the definition of additional commands in the
interpreter.  See the latest interp(n) documentation released in
Tcl 8.4a3 for a complete list of these commands.  A nearly complete
list is in the library(n) man page.

http://www.purl.org/tcl/home/man/tcl8.3.2/TclCmd/library.htm

If you just need an internal command interpreter without all the
additional comands provided by Tcl_Init(), Tcl can provide
that without needing Tcl's script library on the system.  Just
be sure your application that embeds Tcl doesn't call Tcl_Init() !

''Are there additional standard Tcl script library components that are''
''required?  I might venture the guess that you would _need_ auto.tcl,''
''init.tcl, package.tcl, and the encoding directory.  You may really want safe.tcl.  Are there others that are required?''

Note that the commands added by Tcl_Init() form the fundamental
basis for both Tcl's autoloading and package loading facilities.
So, if your purpose in embedding Tcl is to gain access to Tcl's
rich universe of useful packages (including Tk!), then yes, you
must have a working Tcl_Init(), meaning you must have some means
of accessing (or replacing) init.tcl and the other files in the
Tcl script library.

Solving this problem is a major part of the various techniques
used to create "single file" Tcl applications [[see "[Transforming Tcl scripts into binary code]"]].  Let me know
if you need pointers to the lists of those.  They get posted
here about weekly.