const gchar* vs gchar *

[Geert Janssens]

And now a question to show that I never had a formal c/c++ education.

Are the below functions equivalent ?

void funcA ()
{
     gchar *varA = g_strdup ("Test");
     <do something with a>
    g_free (varA);
}

and


void funcA ()
{
     const gchar *varA = g_strdup ("Test");
     <do something with a>
}

I'm mostly wondering if the second function would have a memory leak or 
not. If varA is defined as a const gchar *, will the program 
automatically free the memory allocated with g_strdup ?

I don't expect so, but I'm seeing mixed uses in GnuCash and want to 
determine for once and for all what is the proper way to handle this.

Geert