Mass accuracy is relative and as always depends on the calibration.  Two competing processes occur as the flight time increases.  First, the temporal measurement precision (t/Δt) increases because Δt is a constant that is defined by the digitizer and is independent of the flight time t. Second, the measurement becomes more susceptible to experimental drift of the power supplies and electronics.  The spectrum to spectrum flight time variation of singly charge bovine serum albumin (BSA⁺) is about 7 ns while the flight is about 1.4 ms . That is about 5 ppm.  That will get better—it’s only a prototype.  So with external calibration the mass accuracy is about 10 ppm.

With internal calibration, it’s completely different.  Electronic drift and ripple aren’t really serious issues in this case.  The following spectrum of a biotinylated streptavidin complex provides a case in point.  The peak on the right is the complex and the one on the left is the complex minus a 246 Da stabilizer molecule.

How do we know it is a mass difference of 246 and not, say, 244?

The raw data makes this abundantly clear.  The following is the raw data from the streptavidin complex peak.

Next is the raw data from the streptavidin complex minus the stabilizer.

The location of the centers of the peaks is obvious.  There is exactly 2699 ns between these peaks.  In this mass range there are approximately 11 ns for each nominal mass.
If the mass of one of those peaks was known to the nearest 0.1 Da, then the accuracy of measurement of the other would also be to a 0.1 Da because the centers of the peaks can be identified to the nearest ns.  That is 1.6 ppm.  This exceeds FTICR ability to define the nominal mass of intact proteins in this mass range by more than an order of magnitude.  Moreover, better digitizers with 100 ps resolution and 6.7 ms of internal memory at that resolution are commercially available.  Sub ppm mass accuracy should be possible.

Do we need to average to obtain statistically relevant data? 

No, we do not.  Unlike normal Q-TOF MS systems, ours is an ion trap based system.  Our digitally driven linear quadrupoles can be used as ion traps.  Ions can be sampled into the trap until the population is large enough to be statistically significant.  Each of the spectra that you have seen has an ion population of approximately 1 million; therefore, each spectrum is statistically relevant.