Yes, but it would cause another problem. The brightness of the digit would not be the same for all values. If a "1" was being displayed, those 2 segments would be much brighter than if an "8" was displayed.
It's better to simply increase the segment resistor values so that the digit pin current remains safely under 40mA even when all 7 segments and DP are lit.
Alternatively, put your 270R resistors on the digit pins, and no resistors on the segment pins. But then you have to multiplex segment-by-segment instead of digit-by-digit. SevSeg library can be configured to work in that way.
You are saying that Timer2 is refreshing the multiplexed display unit. Timer2 is not a processor/MCU. How can it enable/disable the cathode/anode pins of the digits successively? This is what happens:
You have four digits in the multiplexed display unit. The refreshing of each digit must be done within 20 ms which insists to keep a particular digit on for about 5 ms. Instead of using delay(5) function which blocks the MCU, you have used Timer2 to provide 5 ms time tick in the background. You could use Timer0 driven millisCounter/millis() (@david_2018#11) for this delay purpose and keep both MCU and Timer2 unblocked.