Yes it would affect the truing job, but no it probably wouldn't affect accuracy. Part of the truing process is recutting the cocking ramp in the bolt body so it's in time with both the lug ramps and the primary extraction ramp. One or all of those ramps being out of time with one another is the primary cause of the hard bolt lift common to Savage rifles.
The cocking ramp basically dictates how far the firing pin is retracted (cocked) and at what distance it is held at when in the cocked position. From the factory the cocking ramp greatly over-retracts the firing pin before letting it back down to it's held position which also contributes to the harder bolt lift.
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