I have PV + 2 Tesla Powerwalls. The Tesla batteries provide whole-house backup in the event of a service interruption, and the system releases stored solar-generated power into the evening after the the solar system can no longer charge. I'm in Los Angeles, so for much of the summer I am 100% solar powered.
Regardless whether you are running off PV or batteries power, you are getting your power from those sources via an inverter. The PV and Tesla systems work together but each has a dedicated inverter. SQ apart from noise is slightly-improved over LADWP grid power some of the time. Or it is benign. Never worse in terms of the usual considerations for tonality, dynamics and whether the systems are more or less musically convincing. However, I run two discrete hifi systems in my house and one of them suffered eruptions of new noises upon installation of solar, and some additional noise was introduced by the subsequent installation of the Tesla batteries. The two systems were not equally affected. One had minor new noise issues that were quickly handled. The main system, which happens to be located directly under the PV array, accumulated new noises that were not easily squelched. I believe non-line-borne RF from the PV array was at least half the problem, and line-borne noise from the inverters made a substantial contribution. In the more affected system, I had to abandon SET power amps and an active linestage. I also had to replace my ZYX Artisan phono preamps, which are built into unshielded wood boxes.
However, I made some necessary changes to the gear and am back to a quiet system. I hear no evidence of any peak power limitations from the batteries when they are powering the house. But then, my systems are built around Zu speakers of 101db/w/m efficiency, so I also do not need nor have big, current-sucking amplification in either instance.
It would take some research into inverter alternatives that also will pass muster with your local power company. LADWP is making up its regs as it goes along, so very small things can grind PTO approval to a halt. I didn't have an interest in disturbing that process. The inverters are considered the most vulnerable part of the system, and the most likely to require replacement within a decade or so. Anyway, my completed system functions smoothly and seamlessly, orchestrating the distribution of PV-generated power to my house, to to charging batteries, and back to LADWP as well as the batteries' discharge to power the house, and when to run directly and solely off the grid. It's all observable real-time in an app on my phone. Slick.
Phil