No a Pokémon with Telepathy will still get hit by Teeter Dance if one of your Pokémon uses the move.
"A Pokémon with Telepathy avoids all damaging moves used by its allies in Double and Triple Battles. This includes attacks with multiple targets (such as Discharge), as well as attacks exclusively targeting an ally with Telepathy (such as Thunderbolt). However, it is not protected from its allies' status moves (such as Teeter Dance or Confuse Ray)."
If you want to use Teeter Dance in a Double or Triple Battle without effecting your Pokémon too, I recommend giving your other Pokémon Protect. Teeter Dance is not on the list of moves that can bypass Protect.
Hope I helped :)