You don't say if you already know the name, but I'll assume since you
want to know "does this tree exist" that you already know the name it
should be using.
In which case, you can use llength on the return value of [info
commands] to determine if the tree name exists:
$ rlwrap tclsh
% package require struct::tree
2.1.2
% set t [struct::tree]
::tree1
% info commands ::tree1
::tree1
% info commands ::tree2
A zero llength would mean "no tree of this name". A non zero would
mean "a tree of this name" exists.
Now, technically, this is "does this command exist", but as the tree is
a command, you'd then know the tree existed (provided you didn't create
a command of the same name that is not a tree).
But I also have a sense that your request is for a different problem,
one you've left unstated. So what is the issue you are really trying
to solve?