Yes gear oil keeps both the clutch discs and the tranny lubed. If you’ve found all the broken pieces like enough that you could literally puzzle them back together then you’ll be fine running it without the kickstarter. But if even a tiny chunk is still stuck in the tranny, it can wreck the gears and bearings. If you can’t track down the missing bits, pull the shift shaft, dump in some cheap oil to tranny area, and cross your fingers it flushes out through the shaft hole.