If by path following you mean route following the answer becomes something my team has dealt with in the past. In an independent swerve chassis each wheel can move individually. For following a pre-programmed route/path this can cause some difficulties with wheel alignment. if the wheels start the match slightly off from straight this can cause your robot to not perfectly follow the route you set. In 2015 the slight variations in wheel alignment between our modules prevented us from performing a 3 tote auto successfully. However 3360 was able to successfully perform a 3 tote auto that year(
link to show amount of precision required). The key difference was the amount of precision our two harvesters required. Depending on the slop present in your swerve drive system you may have slightly less precise driving in auto.
Slop effects both tank and swerve drives systems. This is part of the reason why you can see teams driving their robots back and forth across ground before a match (helps with lining up the robot and making sure the gear systems are matched up reducing the effect of slop). It affects swerve systems slightly more in that you have two separate gear systems that can be effected by slop(drive and turning vs. just drive in tank).
Additional note on path following for swerve:
In tele-op following a path is relatively simple as any of the minor differences in wheel angles can be dealt with by your drivers.
Tldr;
Auto: Depends on slop in your gear trains and how closely you need the robot to follow the preset path.
Tele-op: you should be okay.