Most Regulators will self regulate permanently when overloaded. Some will have an inbuilt fuse, some will just fry the circuit board &/or relays.
200W @ 12.6V = 15.87 Amps (theoretical max output, more likely will max a lot lower, 12 or 13 amp.)
Way over the rated 10 amp reg, will fry it for sure the first time it gets a strong burst of sun.
I would use a 15 amp minimum, however to be safe I would use 20 Amp reg, 20A rated wiring & fuses.
There is a reason why 10A regs cost less than higher capacity regs. Component load rating.
BTW, don't forget to keep an eye on the electrolyte levels of your flooded cell Lead Acid batteries, especially if the regulator/s you choose are not programmable. Long periods of higher than optimum float voltage can off gas a lot of hydrogen, make sure adequate ventilation to prevent gas build up.
The cheaper not programmable regs may float & or boost charge your batteries at higher or lower voltage levels than optimum, so keep an eye on the voltage as well. Float, Boost & Absorption (if available)
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