That could possibly do it. One thing that's different about Trace/Xantrex inverters is that they actually synchronize both voltage and frequency with the generator, and that gives them the capability to do generator support. Meaning they can use a generator to take over heavy loads and if the generator can't supply all the power for the load the inverter will supply what the generator can't. This allows us off-grid folks to use much smaller and more fuel efficient generators. Outback and Magnum inverters don't have this capability, however, Magnum is coming out with one in a few weeks that does have generator support.
So, because of this, the Trace/Xantrex requires stable power from the generator. If the gen is surging (or undulating as you call it), that means the frequency is constantly varying and the inverter won't sync with it.
During the final stages of absorb charging, the Trace/Xantrex does load and unload the generator to "test" how well the bank voltage holds up during the unloading part - this is how it determines if the bank is nearing the charging end amps. If the bank drops too much in voltage when it unloads the generator (and reduces the charging amps to below the ending amps setting), then the inverter goes back to absorb charging for a bit more time until it decides that the bank voltage is holding up when it drops the amps below ending amps.
This "pulse" type charging is actually great for the batteries - they love it. But again it requires a generator with a stable governor because if it starts to surge when the inverter does this, the inverter will spit it off and see if it evens out and becomes stable.
Edit:
The new inverter Magnum Energy is coming out with is called the MSH4024RE. It has dual 60 amp AC inputs, and generator support. The first ones will be 120V only and are non-stackable. It is in beta testing yet, but very close to production release. It will be Magnum's version of the venerable Trace SW.
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Chris