Yes, of course, on both accounts. The first isn't a problem; simply charge the battery fully before starting the system or start with a completely discharged battery. As for the second, I cannot say; I don't know how much variability in capacity there is in small batteries.That would also require starting with a known level of charge. And a battery that actually has the full capacity that it should.
This method of monitoring SOC is widely used in backup electrical systems like Tesla Powerwalls and SMA Sunny Island inverters.