GNU Parallel uses ssh for remote execution, so the $PATH is the same as you would see when you run a non-interactive ssh session:
ssh server echo '$PATH'
parallel -S server --onall {} '$PATH' ::: echo
The reason you see a different $PATH when you log in is that interactive sessions may set another $PATH.
You can force parallel
to copy an environment variable using --env:
parallel --env PATH -S server --onall {} '$PATH' ::: echo