If it does, get it in writing.
There are so many times that buyer clients call me after closing to let me know that the seller took something they thought was supposed to be left. Sometimes it is clear in the agreement; sometimes it is ambiguous, it was in the listing but didn’t make it into the agreement, or in the negotiating process it fell out of the agreement and the buyer didn’t notice.
Ultimately, the agreement rules. If you want to have something included, the only way to ensure that the seller has to leave it – or compensate you – is to put it in writing.