While every team would love a shot at the GC of the TDF, I bet there are teams that know they don't have a prayer. So what do they do?
Well they could win the polka dot Jersey or the green jersey if they have a rider that can pull it off. They could win a stage. They could have a rider wearing the yellow jersey (or one of the other jerseys) for a stage or more. They could have a breakaway that lasts most of the day. These are all accomplishments that garner much attention for the rider and the team, well they are accomplishments outside the US. Here we only know of the GC and only at the end of the race.
Not to get into the pro or anti Armstrong debate but most Americans think he dominated the TDF more than anyone in history because he won seven TDFs, but there are others on this planet who think someone else (who won five TDFs) dominated more when racing in the TDF because he wore the yellow jersey for more days in total while in the race. I guess it all depends upon how you define "dominate".