What are you asking? If third party voters want to contest all congressional seats? Or if there is a third party candidate who contested congressional seats?
No matter what you are asking, what party are you asking about? 3rd party isn’t a party itself, there are no general 3rd party beliefs and actions. Are you asking about the libertarian party, the largest third party by registered voters? Or the Green Party who had Jill Stein take the most 3rd party votes this year? Or some other party?
You’re right, but voting third-party for presidency and your own states’ congressmen are not mutually exclusive. You may vote third-party for both.
Even without a supporting legislative branch, a third-party president may have influence through vetoes alone. Presidential vetoes on bills have historically had high success rates to get congressional bills denied. There is also always the off-chance that something like H.R.5140 gets passed, and a lot of politically relevant seats become available for a third-party president to assign bodies into without question. Not likely, but nothing will ever even have the chance to change if you continue to vote for the primary two parties