This is practically impossible for a couple reasons. Your routing plan doesn't allow for any cooling of the beer line, which would make the system virtually useless and would likely cause some sanitation problems as the beer would undoubtedly go over 50*F. If you did try to add forced air cooling the small undercounter fridge simply wouldn't be able to cool 15' of beer line even if you added a direct route air tunnel.
A glycol system would work, but at that expense it would almost be cheaper to buy an outdoor unit.
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Always do sober what you said you'd do drunk. That will teach you to keep your mouth shut.
Ernest Hemingway
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