Determining this is simple, we just run the GNU Hello program's configure script under strace like this:
strace -e execve -f ./configure 2>stderr.txt > stdout.txt
This puts all command invocations of the process and its children to stderr.txt. Then we can massage it slightly with Python and get the following list of commands.
This list contains a total of 49 different commands including heavyweights such as diff and gawk.
Thus we find that the answer to the question is no. Configure requires a lot more stuff than just shell plus make. In fact it requires a big chunk of the Unix userland implictly.
It could be said that all of these programs are not strictly required and that configure could (potentially) work without them present. This is probably correct, but many of these programs provide functionality which is essential and not provided by either plain shell or Make.