I do not think that it is true that adding or removing an embedded picture in a file effects the length of the audio part.
It influences the total size of a file.
But as tag data and payload data should be separate, any difference in play length can come only from players that do not interpret the tag part correctly or from corrupted header data.
Also, for files with variable bitrate sometimes a certain player uses calculations that are different from other programs. So differing lengths could be the result.
But if a file that shows no length at all - as the OP stated - then the file is seriously damaged and needs repairs.
Ways to repair files have been mentioned in this thread.
See also