It's probably in the queue to be processed, but I assume they most likely work from when it was sent off rather than when they get round to it in terms of enforcing the deadline. Doesn't mean they won't fill up before getting to yours if it's at the bottom of the pile, though.
Ring them if need be. They don't volunteer as much info as I might like, but are pretty prompt if you actually ask them.
I was told the e-induction comes later though - what paperwork have you sent in? Tenancy agreements and such?