Obviously, the theoretical answer is yes, given an advanced-enough exploit. But let's say Apple is unaware of a specific rootkit. If each OS update is a wave, is the installed exploit more like a rowboat or a frigate? Will it likely be defeated accidentally by minor OS changes, or is it likely to endure?
This answer is actionable. If exploits are rowboats, installing developer OS betas might be security-enhancing: the exploit might break before the exploiters have a chance to update it.
Modern iOS has an incredibly tight secure chain-of-trust bootloader. If you shut your device to a known-off state (using the hardware key sequence), on power on, you can be 99.999% certain only Apple-signed code will run all the way from secureROM to iOS userland. The exception is if the secureROM is somehow compromised and exploited remotely (this requires hardware access at boot-time so I don't buy it).
So, on a fresh boot, you are almost definitely running authentic Apple code. The easiest path to a form of persistence is reusing whatever vector initially pwned you (malicious attachment, website, etc) and being clever in placing it somewhere iOS will attempt to read it again on boot (and so automatically get pwned again).
But honestly, exploiting modern iOS is already difficult enough (exploits go for tens millions $USD), persistence is an order of magnitude more difficult.
Apple bought out all the jail breakers as Denuvo did for the game crackers.
Do you have sources for these statements?