Yes, there is an api. You can find some example code in the online developer help http://help.qlik.com/sense/en-us/developer/#../Subsystems/Workbench/Content/BuildingWebsites/API/Methods/getAppObjectLis…
I haven't seen any extension yet that returns the number of sheets though
Users can know how many sheets are in an app by accessing the sheet navigation menu:
Also, I don't get why users would really need to know exactly the sheet number they're in unless there is some kind of "forced" navigation the users need to go through, start to end.
If that is the case, you could develop a really easy Extension to draw a text with the total number of sheets or the actual sheet ID with a few lines of code.