I don't know... depends on the equipment, input voltages, voltage regulators, how you have it rigged up, ect.
Batteries , as a general rule, are pretty tolerant about voltage issues as long as it is DC power, and the input is above a certain threshold voltage wise for charging. As an example the whole Jericho TV show thing with the wind generators and needing some sort of speed regulator so the voltage is "correct" only applies if they are NOT using batteries and running the wind generators directly into a inverter to power the town. IF they have batteries to run into the batteries will act as a "filter", taking in any voltage over threshold and storing it and then putting out the batteries rated voltage into an inverter. It would be nice to have a voltage regulator ( off a car, or better a heavy duty regulator off a truck or the like to smooth out the input and prevent feed back ) but not a critical item. Of course if they used real world stuff in Jerchio then they wouldn't need to interact with New Bern at all, and there goes the plot.
Read the inverter manual and see what it says about running it while the batteries are being charged and if you need a voltage regulator between the batteries and the inverter to protect the inverter.
Likewise you might need to protect your panels from current flowing back up into the panels, this is one of the things the panel regulator/controler is supposed to do, so read and see if it says anything about that...personally I would disconect the panels at night and use the generator with the panels disconected to charge the battery if I didn't know for sure about the batteries discharging when thru the panels when the sun wasn't shining ect.
The batteries should be marked with voltage and amp hour rating somewhere on the case.
the simple fact of any system is you can get more out than you put in... if the panels are rated at 45 watts and you have 5 hours of sun then you can use maybe 150-180 watts a day if you want to maintain the batteries at full charge( you lose some watts in the charging process as heat , batteries and wires all get warm from the missing watts).
That shade issue is critical as is the orientation of the panels. Look at it this way , lets say you panel is 8" x 12" for example. Now imagine a 4" x4" square of light shining down on the panel directly square on the panel. Now imagine moving that light source to one side so the panel is at an angle and the light spreads out, still 4" wide but because of the angle covering the whole 12" long lenght of the panel ( try this with a flash light so you can visulize it better). when the light is 4"x4" straight on to the panel it only cover 1/6th of the panel and makes, lets say, for example, in this case 4 watts and the panel can potentially convert that light , if each of the possible six 4" squares had the same light, into 24 watts..... but at the angle where the light covers a 4" x 12" section of the panel you still get 4 watts from the light, but it now takes half of the panel, making the panel potentially capable of only 8 watts with angled light. Throw in an inverter that sucks up 25% of any power coming thru it converting it to AC and you only get 6 watts into the light bulb by the time all things are said and done.
Okay now about that generator , undoutablely that 1000 watt rating is the 120 volt AC output rating. Divide the volts ( 120) into the watts (1000) and you get amps + about 8 amps. I suspect that in DC mode ( battery charging mode thru the DC connector for the battery cables on the generator) you are still getting about 8 amps. Amp hours are the unit of storage/ measure of electrical power, watts are quanity and volts are "pressure" .
http://www.powerstream.com/Amps-Watts.htm
You can't get something for nothing. Your 45 watt panel at 24 volts is about equal to 225 watts at 120 volts , or put another way 200 watts of solar at 24 volts equals your 1000 watt generator at 120 volts. Anyway you cut it it takes about 1 horsepower of gasoline engine to make 500 watts at 120 volts or 4 amps. Those small electrical chain saws for example can run as high as 13 amps with intial startup requirements lose to 30 amps for a very brief moment( high start up draw is a characteristic of electrical motors). That why gasoline generators are often rated something like 1000 watts/1800 surge watts. Doesn't mean it actually out puts 1800 watts , just means that a short draw of 1800 watts won't fry it and it will take a moment for the electrical motor it is powering to get up to speed.