Do Search Engine Spider's submit POST forms?

The Googlebot can submit forms, but it generally doesn't unless it can detect a reason to do so.

So from the links, if your translations were AJAX'd and built properly, Googlebot may very well submit the form to see what the results would be. However, this behavior (especially on POST), is not guaranteed and you should probably use GET to make things more accessible to the robots.

Bing absolutely does. Before I told it not to it would continually submit both a contact form and a survey form. I knew it was Bingbot because I included $_SERVER['HTTP_USER_AGENT'] in the $_POST information. No other spider ever submitted those forms.

They can and do. I've got a simple email collection form on the front of a site I'm about ready to launch. I just received a submission from that form from IP 66.249.73.214, which is a GoogleBot IP.