What’s the probability, that a user is online? If a user wants to buy stuff with real value or your game wants to show new non-cached ads, your game also needs an online connecting. I don’t see a problem with always on.
If you really want to prevent offline cheating, you need to get the time from a monotonic clock. Many VC versions are buggy and do not provide monotonic clocks. This is against the standard, so you have to test your compiler/runtime or switch to a conforming one.
Take a read about it here:
If your system clock is not monotonic, it wouldn’t help, as you are just storing the start time and compare it to the system clock, right? Do you get the system time through SQLite? Is it monotonic?