It is possible to connect an inverter directly to a regulator/controller as long as the total amps being consumed by the inverter and anything plugged into it doesn't go over the max amp rating of the controller. It is also essential that the regulator/controller can supply constant and stable 12-14VDC power.

For example if you have a 12V controller rated at 12amps, and you connect a 300W Inverter which consumes 0.5Amps when turned on, you would be left with 11.5A to run your appliances (roughly 135Watts—11.5A * 12.0V=138W). If however you tried to use more than the power available from the regulator, you could cause damage to your inverter as well as your regulator/controller. Due to changing sunlight conditions providing a variable voltage supply, and due to it being hard to monitor exactly what power you are using, it is highly recommended to connect your inverter directly to your battery (or battery bank). A battery (or battery bank) is the most stable source of DC Power.