Yes. The trouble with "shut up and multiply" - beyond assuming that humans have a utility function at all - is assuming that utility works like conventional arithmetic and that you can in fact multiply.

There's also measuring and shut-up-and-multiplying the wrong thing: e.g., seeing people willing to pay about the same in total to save 2000 birds or 20,000 birds and claiming this constitutes "scope insensitivity." The error is assuming this means that people are scope-insensitive, rather than to realise that people aren't buying saved birds at all, but are paying what they're willing to pay for warm fuzzies in general - a constant amount.

The attraction of utilitarianism is that calculating actions would be so much simpler if utility functions existed and their output could be added with the same sort of rules as conventional arithmetic. This does not, however, constitute non-negligible evidence that any of the required assumptions hold.