<p>I see plans for various spool holders, either for PLA in the open, or for whatever filament in a dry box, that use 608 bearings. Elsewhere, I see warnings not to oil your filament to make it go through the extruder better, because problems going through mean something else is wrong, and it's better to fix the other thing. So, if I use the 608's, will oil leak on the filament, and is this bad?</p>

Typically, oiling a filament would mean to use a vegetable based or non-petroleum type of lubricant, possibly even PTFE (teflon) or silicone. Those materials will not damage PLA filament.
Oiling filament is not the haphazard application of lubricant, however. One drop on the filament sponge guide will last a rather long time and should be given sufficient time to distribute itself in the sponge, helping it along by alternately squeezing and releasing the sponge.
Ball bearings of the type you've described will not have oil, unless otherwise modified by the user/owner. The bearings are packed with grease which will not leak out under normal circumstances. Running the bearings at high speed will cause the grease to thin a bit and perhaps drip or if hot enough will "sludge up." If your bearing grease turns to sludge, the bearing has already gotten hot enough to melt out of your plastic fitting.
For spool holder applications, you can clean the grease from the bearing with a suitable solvent (denatured alcohol, acetone, soap and hot water in a pinch) and expect little impact on the drag. The spools rotate at such slow speeds and under such small load that the bearings alone will work nearly forever. This recommendation is void in dusty environments.
With respect to oiling the filament, it's not a bad idea to have a sponge dust catcher that has no oil just as the filament enters the last open location. My bowden extruder system is nearly enclosed and the sponge sits at the very edge of the spool, while a direct extrusion system would have the sponge at the entry to the extruder gears.