Rushing blink dagger is generally the way to go on Tidehunter. You want to get blink after arcane boots as soon as you can, then refresher, pipe, mek, or force staff.
However, Tidehunter is rarely in a position to be farming away. Getting courier for your pub game team wouldn't hurt before the horn. Buy that, a (very valuable now that it is 3 armor) ring of protection, and tangoes, and you're good to soak up experience offlaning getting levels in your passive and your anchor smash to farm the ancients, where you can get 6, and the blink dagger will fall into place after using your ult somewhere.
Unless... you're buying all the team's smokes, wards, counter-wards, dust... especially if your level 6 gank or ancient stacking didn't go swimmingly. There should be someone, if not two other players, in your game, who are more apt to get wards throughout the game. So, short answer (at the end of a long answer): no, Tidehunter isn't a support role.
Dependent on the four people you end up in a game with, well, you might be delaying that dagger for some wards if no one else will.