With "daisy chaining", do you mean a series connection or a parallel connection. The obvious would be parallel, but in general the term refers to series connections. If it is a series connection, you push up the voltage, and I'd be surprised if the charger or the inverter works.
Parallel is a different matter: you keep the voltage constant, but you increase the total battery life. In that case it might work. Yes, in certain instances it will work, but in others not. If a lead-acid battery is not charged according to the correct charge profile, it's total life can be decreased. With multiple batteries charging off the same charger designed to charge only one, you forego the advantages of a intelligent charger that takes the battery's characteristics into account. I.e. it will not monitor the batteries' temperature, it will not decrease the charging voltage at the correct time, etc.
Also, I presume that your current limiting is on the inverter side? If not, be careful of overloading the inverter. Cheapie inverters will not necessarily have overload protection, and if you overload it it might just join the South-African workforce in a violent strike action. The components inside (think inductor, caps, transistors) are designed with a few criteria in mind, amongst others are: cost, current rating, switching time. For cheapies, the trade-off between cost and current will be in favour of cost, meaning that they can't handle as much as the batteries provide. Actually, the current limitation applies to ALL inverters, but you're more likely to meet it with cheapies.
I tried to type in laymen's terms - please excuse me if you already knew all this. I'd just prefer not to have someone reading this think that he can driver his house solar/battery system from i.e. a Telkom UPS...