Having the shrine inline with the lilypad of fertility, so 1 above the farmland, causes the particle effects to generate fast on the lilypad but the growth effect from the lilypad stops working entirely, or at least didn't trigger over a few minutes.

ModPack
ATM6 v1.5.2

More playing with this, sometimes the lilypad keeps working as normal. Sometimes it stops working entirely. Sometimes there is a large delay for the effect of the lilypad. It doesn't seem to matter which order the lilypad and the shrine is put down in.

It doesn't seem to be a problem with the growth shrine as I just had a lilypad alone and it wasn't working.

I tested a bit more and I really think it is an issue with the lilypad itself, I would recommend opening an issue to the correct project.