is a voltage regulator required for atmega328p when powering from boost converter at a set voltage?
is a voltage regulator required for atmega328p when powering from boost converter at a set voltage?

No it is not.

The ATMega is "just" some logic circuits in a chip.

So is the CPU in your PC and in your smartphone. Both of these are powered directly from switched regulators (usually buck converters but that doesn't matter that much) and they work fine!

As long as you keep the supply voltage of the ATMega chip within the specified limits (see the manufacturer's datasheet, from my memory it is 1.8 V to 5.5 V) then it will work as long as there is not too much variation (ripple) on the supply.

To keep the ripple in check, any boost, buck and linear regulator has at least one decoupling capacitor across its output. The ATMega chip also needs it's own decoupling capacitor. It is good practice to place at least one near each supply pin.

The accuracy of the supply voltage is not that relevant. The logic will work just as well at 3.456 V as it will on 3.3000 or 5.0000 Volts.

The only exception can be if you use the build-in ADC of the ATMega. This ADC can use the supply voltage as its reference voltage. If the supply is not accurate then the ADC's output data will not be accurate either.

There is a build-in more accurate reference for the ADC that can improve this.
You can also use an external reference voltage if you like.

Also if you would use the PWM output function, filter the PWM signal and want it to be accurate then also it will be as (in)accurate as the supply voltage.

But in general, if you need this then you would know and take precautions.

Oh and there is no reason to assume that switched regulator (boost or buck) are in any way less accurate than linear regulators. It depends on the model (chip, circuit) you're using and if you calibrate it or not (measure the voltage with a known accurate meter and then adjust to the right voltage). Both linear and switched can be as bad or good as the other.