Can you use sweet potatoes in a no-bake pie?
Yes, I think you could successfully substitute sweet potatoes, with perhaps a few considerations.

Peel your sweet potatoes and steam until tender, then mash and whip by hand, or with a food processor or blender.

Sweet potatoes will be somewhat sweeter than plain pumpkin, so adjust any sweeteners in your recipe accordingly. Canned pumpkin may also have a higher water content, so be aware of that as you assemble the ingredients.

Note that canned pumpkin pie filling is different than plain canned pumpkin, in that it has sweeteners and spices added. Depending upon which kind of pumpkin your recipe is calling for, rely on your own sense of taste to fine-tune the sugar and spice.