You could check - have JavaScript that populates a hidden form field with a specific value after the page loads. Then, when the page posts back to the server, check that hidden form field the expected value. If it is not there, that means the JavaScript didn't execute.
As to whether you should assume it is spam is another story altogether, and one that has no certain answer, really. You could simply have a <noscript> tag and have it indicate to the user that their submission will not take unless they enable JavaScript.
Once you have JavaScript running, however, the spammers will just use another workaround for that. :)