I believe it won't... Polylang modifies any url in the search form. That's a bug. Only the url of the form statement should be modified.
Could you try to edit the file polylang/include/core.php at line 713 and replace
str_replace(trailingslashit($this->home), $this->get_home_url($this->curlang, true), $form) :
by
str_replace(trailingslashit($this->home), $this->get_home_url($this->curlang, true), $form, 1) :
I am not sure, but maybe the issue comes with the combination WP3.6 + Polylang 1.1.x as the search form function has been modified in WP3.6 and I (tried to) adapt Polylang starting from 1.1