Sean,

two ways come to mind:
1. Write a small perl script which in essence executes SCM commandline commands:
first, do: scm login -u <user> -P <password> -r <Server URL> -n jazz
examine the result of
@result = `scm list remotefiles -r jazz --depth - <Stream / Stream Snapshot> <Component>`;
by e.g.
$number_of_lines = @result;
print "$number_of_lines Files / Folders in Component\n";

2. Load the component to disk from a repository workspace
Use OS means of determining total number of files. E.g. on windows open commandline to top directory and issue
>dir *.* /s

If any of this answers your question please mark the answer as accepted.
- Arne