No. Aleuts—who often call themselves Unangan or Unangax̂—are a distinct Indigenous people of the Aleutian and Pribilof Islands, not the same group usually meant by “Eskimo.”
In common and scholarly usage, “Eskimo” has referred mainly to Inuit (including Alaska’s Iñupiat) and Yupik peoples. Aleuts are generally excluded from that label, even though Unangan and Inuit–Yupik languages belong to the same broader Eskaleut (Inuit–Yupik–Unangan) family.
The Alaska Native Language Center notes that people of the Aleutian and Pribilof Islands prefer Unangan/Unangax̂ rather than Aleut, and that “Eskimo” is fading as communities use their own names.
Source: Alaska Native Language Center — “Inuit or Eskimo: Which name to use?” (University of Alaska Fairbanks)