It is generally a bad idea to e2fsck a file system while the file system is mounted (the man page mentions one specific situation where it is safe:
-n given, and
-L not given, and even then it is not recommended).
However, what would happen if a file system check is in progress when some other process tries to mount the file system read/write?
Obviously e2fsck would likely go haywire and complain about dirty blocks all over the place, particularly if the file system then sees active use, but absent administrator intervention to attempt to correct any such "errors", is there any risk of data loss or file system corruption?