UIF does try, but the reality is that they do tend to work to their own time-table that seems to escape us mere mortals - no manner or amount of terse phone calls to the wonderful folks at the UIF offices seems to get a reaction.
I am always nervous to "rely" on UIF, as they can be very unreliable - but sometimes do pay when they are supposed to.
A really good idea is to look at your accounts that you have to pay over your maternity leave and see if you can get them deferred.
I deferred my car payments and my other two kids school fees over my maternity leave - so that in the event that I was stuck high-and-dry I would not be drowning in debt-collectors. I made arrangements with my bank should I need access to additional revolving credit - I really planned as if the world was going to come to an end.
Considering planning for the worst case scenario, but if it goes well, then great, but rather plan for payments not coming in, in the event that they run late or what ever.