Complicated answer.
Could the equipment you have provide backup to a house running moderate loads for while - yes.
As others have indicated it would really depend on what your current average loads are and how long you want to be able to support those loads.
More technical answer:
1 - If you want to use the 6000XP to take power from the grid bypass and provide power to the house when grid goes down, there are certain considerations:
What is the supply amperage - the "main" breaker in your electrical panel. The 6000XP will only handle a 50A pass through load (I think that is the max). So, if your main break is a 50A or less, you could probably get away with it.
I don't think that in most municipalities this is an accepted solution though.
2 - Instead, what you might want to do is set up a critical loads panel-
Power comes into your main panel - then to the 6000XP - then feeds your critical loads. When power goes out your critical loads stay running. When power is up, the 6000XP bypasses the inverter and powers the critical loads.
This is one of the easier methods, but it does require rerouting your critical loads to another panel - electrical work.
3 - Another method is to have a transfer switch that allows you to turn off the mains power during a power outage and turn on a feed from your inverter back to your panel. (not my favorite method as for me it involves too much remembering what breakers to flip). This would also require an electrician and tends to be a more manual method. There are some relatively expensive automatic transfer switches as well. Just depends on your budget. The photo in this post shows an example of this set up. https://forum.eg4electronics.com/community/postid/12505/
Another technical point about your equipment and proposed idea.
I should be able to power everything with a single 6000XP. I also have the generator, which I would connect to the Chargeverter then to the 6000XP's generator input to ensure that I am only sending "clean" power to the system.
The chargeverter would not plug into the gen port of the 6000XP. That port is for AC into the inverter(or a smart load out if I understand correctly). The chargverter outputs DC. You would connect the chargeverter to your batteries instead.
You can check out this PDF on the EG$ site to get some ideas of how to do Suggestion #2 above.
EG4 6000XP System Wiring Diagrams_v1.2
So, some questions for you:
A - as others have indicated - do you have a rough idea of what your power usage would be?
B - an idea of how long you would be willing to go on battery only before switching to gen power?
C - What size is your main breaker?
Hope this helps some and best of luck.
Please keep us posted with how it goes or if you have questions.
JB