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If the liner can fit in that tiny house, then you're sorted.
It's a good idea to run it from the plastic cable guide on the BB to the very top of the derailleur clamp, but ensure to leave enough room for it to shift to the largest chainring.
If it doesn't fit however, it's best to just spray GT85 through the hole if possible every once in a while, but it's rare for it to get murky enough to hindrance shifting performance.
Alternatively, I may recommend good mudguard to keep your drivetrain from getting sillily murky.
How does that work? liner from cable entry point to frame up to just short of cable clamping point to the derailleur? What keeps the liner from moving when shifting, friction against the BB cable guide?
Edit nvm, found a video showing how it works. I'll give that a try. Thanks