Without seeing an actual wiring diagram or the equipment itself and how it's wired, it's hard to say. So, based on the info you have provided, and if I understand it correctly, I'm going to say the answer is NO at this point.
A few questions to establish existing status. Most of these can be answered just yes or no.
1. Does 120VAC power go from the shore power receptacle, directly to the block heater switch, battery charger/maintainer, all at the same time?
2. Does 120VAC power also go from the shore power receptacle, directly to some or all of the electrical wall outlets?
3. Does 12DC power go from the battery bank directly to the inverter?
4. Does 120VAC power go from the inverter directly to some or all of the electrical wall outlets?
5. Does the shore power receptacle and the inverter send 120VAC power to the same outlets?
6. Does the inverter and charger/maintainer come on at the same time?
7. Is there a relay/transfer switch or a mechanical selector switch to prevent the inverter and the charger/maintainer from being turned on at same time?
If the answer to #6 is yes, and if #7 is no, then you have a big problem.
The inverter and charger should never be operated simultaneously, and configured so that AC current from the inverter output is looping back into the charger input, which is supplying DC charging current to the batteries, which in turn is supplying DC power back to the inverter input, which is now trying to power the battery charger. If this cycle operates very long, it will destroy your inverter. At the very least it will shut it down if it has the proper self-defense mechanisms, such as an internal automatic transfer switch, high temperature cutout switch, etc.
Now that you're totally confused, here is some more good info:
http://www.doityourselfrv.com/rv-inverter-install-diy/2/
http://forum.solar-electric.com/showthread.php?16719-Off-Grid-Inverter-Battery-Charging