I don't soak pellets in oil. The long end of the line is cut with angle to pock the patch through. The normal process for cleaning looks like this:
Poke the fresh 1" patch and slide it all the way to support pellets.
Drop of oil on the patch
Thread the line through the bore and pull oiled patch through.
Reverse the oiled patch and use the other side for one more pull-trough.
Repeat few more times with clean dry patches.
For first time cleaning to remove factory preserving grease use more oiled and clean patches. For normal cleaning one oiled patch and 3-4 dry ones is enough.
Felt pellets become saturated with oil by themselves after few cleanings, but it doesn't affect cleaning or drying. They are only supporting patch and creating tight patch to bore fit and don't contact bore directly. All the dirt collected by patch and doesn't accumulate in the felt. Works for many years and cleanings until mono fishing line gets nicked and need replacement. Manufacturing the new one is a few minutes job.
Think of long use of pillow with removable, replaceable pillow cases.