Probably not; if I'm not mistaken, HOME, SWSH, and mons received from GO share the same data partition, which is separate from LGPE, PLA and BDSP.
Normally, a mon from GO -> HOME -> BDSP,
It would (1) first have the HOME/SWSH partition, then clones into the (2) partition and gets it's data modified for use with BDSP.
So if you're injecting from BDSP, you are giving HOME the (2) partition, but noticeably missing the (1) partition. And (2) doesn't clone into (1), hence why the ball goes missing.