What happens when there's no space left on SD card?
Open-source is just great. Lets have a look at the source code for SD. Here is what happens on write of a block. 

/**
 * Write data to an open file.
 *
 * \note Data is moved to the cache but may not be written to the
 * storage device until sync() is called.
 *
 * \param[in] buf Pointer to the location of the data to be written.
 *
 * \param[in] nbyte Number of bytes to write.
 *
 * \return For success write() returns the number of bytes written, always
 * \a nbyte.  If an error occurs, write() returns -1.  Possible errors
 * include write() is called before a file has been opened, write is called
 * for a read-only file, device is full, a corrupt file system or an I/O error.
 *
 */


The source code shows that blocks are allocated from the free list and if there are no more blocks the function will return an error.