What would happen if we mounted a file system that e2fsck is already running on?

What would happen if we mounted a file system that e2fsck is already
running on?

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 -c, -l or -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 is there any risk of data loss or file system corruption?