We think it is overkill. We’ve done a lot of logo work and the results we have seen so far have been that small logos are unlikely to ignite and provide extra protection if the fabric underneath is dry. Less protection if the fabric is wet but appears to be the same effect we see with sweat.
A large logo could ignite. We feel ASTM F1506 is right when it says to keep the logo small and I have no opposition to Nomex thread (limited color options) but the backing is really more likely to melt onto a worker than the thread. If you have any concerns, use an arc rated undershirt. We recommend keeping non-FR logos to the size of a business card.
Screen print doesn’t seem to have issues with ignition but has the same issue as any logo. The sweat underneath can cause a steam burn from the sweat. There are “flame resistant” inks but these have not shown any difference in an arc flash. Perhaps someone will have a statistical study someday but this has not happened to date.