I found an excellent article in the archives a few weeks ago.
ftp://gerry.vanagon.com/pub/technical/Refrigerator-Manual.txt/

It says the tube is for condensation.  I had my fridge out Sun and
can say it goes to the pilot light chamber.  The article suggested
removing the cap and blowing air up the tube (he suggested
using a drinking straw) would facilitate lighting the fridge.  That
seemed to be its most useful purpose.

The above is an excellent and complete article about Dometic
fridges.  Only trouble is . . . the last few times I've tried, I can't
pull it up.  Hopefully, it will be available again soon.