As far as I can tell, yes. Tibet wasn't really much taken into account considering the Domino Theory, and when it fell to the People's Republic of China in 1950, Americans were a bit more focused on what was going on in Korea, if they were focused on it at all. It's worth remembering the anecdote that Secretary of State Dean Acheson asked for a map when he was informed that the Communists had invaded south Korea and he asked, "Where is that?"
To most Americans, Tibet would have been comparable to Antarctica in terms of general knowledge, geopolitical importance, and geographic understanding (hell, I think that comparison is still apt. I'm often asked if Bhutan is somewhere in Africa, or to be addressed with simple confusions like, "I thought Tibet was a small place, like the size of New York City... not the size of Western Europe.").
Anyway, I wrote a very long and detailed post here about why Tibet was ignored in terms of Domino Theory. The tl;dr is that aside from the general and specific ignorance in American culture and politics as it regarded Asia, Tibet itself was always always regarded as unreliable at best, and suspicious at worst. When Tenzin Gyatso, the 14th and current Dalai Lama, went to India upon the People's Liberation Army marching on Lhasa, the CIA approached him and offered to support and supply him with money and weapons to push back against the Communists. The Dalai Lama decided instead of expanding hostilities, to go back to Tibet and try to work with the Chinese. The CIA went directly to Khampa fighters from then on, circumventing the Dalai Lama to go right to where the fighting was anyway.
Once the Dalai Lama went back to Tibet and acknowledged Chinese suzerainty/sovreignty (depending on who asks and when) over Tibet, the United States basically abandoned the very concept of an independent Tibetan state. The implication was, of course, that if the Dalai Lama had maintained a strict continuous position of Tibetan independence and sovreignty, they would have supported him from exile, either from India, Sri Lanka, or Thailand.
That said there was a little bit of cultural support, mainly focusing on the religious angle. How Tibet was an ancient society and culture with an old religion that was being destroyed by the godless Communists.
To add to what u/JimeDorje has written about the practical issues, another factor that contributed to American inaction was that the US had already acknowledged China's sovereignty over Tibet during WWII - this was something that Chiang Kai-shek pushed for and got. The British had acknowledged China's sovereignty decades earlier. Neither the US nor the UK had recognised Tibet as a sovereign state. In part, this was because Tibet had not sought such recognition since they had declared themselves independent of China with the fall of the Qing Dynasty until after WWII, at which point Tibet could not be recognised without alienating the Republic of China and breaking wartime promises to Chiang Kai-shek.
In the old agreements between the British and the Qing, the British had recognised China's sovereignty over Tibet, and the Qing had recognised the right of Tibet to autonomy. The ROC was prepared to work on these lines, and in the 1947 constitution, Article 120 read
The self-government system of Tibet shall be safeguarded.
This continued to be the official ROC position. In 1959, Chiang Kai-shek said
The Government of the Republic of China has always respected the traditional political and social structures of Tibet, and upheld the religious faith of its people as well as their freedom to have their own way of life. Today I wish to affirm emphatically that regarding Tibet's future political institutions and status as soon as the puppet Communist regime on the mainland is overthrown and the people of Tibet are once again free to express their will, the Government will assist the Tibetan people to realize their own aspirations in accordance with the principle of self-determination.
which promised autonomy but not independence.
Reference:
The 1947 constitution: https://en.wikisource.org/wiki/Constitution_of_the_Republic_of_China_(1947)