There is no doubt it will happend.
I think the questions are:
When will the features/quality surpass the DSLR we see today (FF and APS-C)?
When will it be cheap enough to send out to the average consumer?
As processors get's faster and better, and batteries get's more power - it's just a matter of time.
Everything get's smaller too.
So when they can pack everything up small enough and make it cheaper/better it will happend.
And in regards to the shortcomings on mirrorless today - i think they will just compensate for those with processing power