Mine does, while my whole rig is running on generator power (shore power) and lets say that both ACs are operating and I have my compressor on while airing up my tires or my wife is using the microwave or hair dryer. When demand from one of the appliances is put on the generator the mechanical throttle must respond to the demand which takes time. If you are monitoring your AC power you can watch it as it descends from 120v to 110v or even 105v. But if you have both legs of your generator or shore power routed into the inverter (Xantrex Freedom 3012) it will attempt to balance the system, it will also supplement the appliances within in a fraction of a second with inverted DC electricity until the mechanical throttle and resulting combustion of the generator is able to provide the necessary current. My whole system is listed below. The reason I said passthrough is because you must have passthrough to have such an assist system. But I would venture a guess that inverters that have pass through wiring will also have this assist feature. And while it is true that there are additional controls, I operate mine mainly from the main control. The system is automatic and sometimes gets in the way of my solar charging in that I don't want to lose battery power that takes so much sun and or LP to make. I find myself turning it off when not needed.
As far as the pricing is concerned, you are correct if he were to install a complete system with solar all at one time. But at the moment he is talking about a generator only for use with his current system. he can do this for $3794 or less, and he might get lucky and find a new one on craigslist. It is true that if he is not gen prepped, he will have to get a transfer switch, $125, a few feet of wire and a junction box. $3925 MAX to this point. He probably needs a transfer switch to do what he is thinking of doing right now, or perhaps he is using his power cord and doing without a transfer switch. He can install a plug right beside this genset and plug in anyway without a transfer switch so hes back to $3794 what would you rather have a 4500 watt yamaha for $3200 + tax or a LP500 for $3794.
Next step is a set of REAL deep cycle batts, not those Marine/RV starting batts. Trojan T1275, 2 @ $250 = $500. These are 8 year batteries at least if not 10 year. The inverter i guess he already owns, but a real inverter/with 4 step charger unit $1400, sub panel with fuses $100, future purchase, but will also require battery cables $200 to $400 and a few fuses, switches $100, a solar charger best $200, ancillary parts $25, $400 to $800 in solar panels.
If he does this work over 2 years he will never notice it. And as far a money is concerned (on the generator) the difference between 2K to 3k and $3794 is small potatoes, The philosophy is that he will always get his money out of the generator and he will be using it to his benefit all that time. A fully installed generator in an RV is worth more than 4k to a potential buyer. he buys it for $3794 its worth at least 6k as soon as he puts it in.
http://www.norwall.com
Gen - $4000 + ancillary installation parts
Inverter $1500-$3000 + ancillary installation parts
Solar panels $300 +++ depending on the size, along with ancillary installation parts.
I could see where installation of these items could easily exceed $1000 in labor. RV labor rates in our area are $125 per hour. So a grand will only get you 8 hours of work.
The "pass through" inverter does not add current to supplement the genny or line voltage.
Pass through is simply that - when not on line the inverter - inverts, when on line shore power "passes through"
What you are referring to is a separate feature on the better, higher end inverters. And requires additional controls.
To the OP - the Honda 3000is weighs about 135 pounds dry, add the weight of 3.5 gallons to that.
Mine will run my 15K AC, but, I leave the AC run with the fan on so at startup up then fan is already running when the compressor kicks in.
And on the hot days the genny will start to balk - as heat increases, efficiency decreases. This can usually be overcome by running the Honda with the economy mode turned off.