A 1 ghz CPU absolutely can run a smooth touchscreen GUI, I think what OP meant is that it's not gonna be capable of running a snazzy Electron interface or some other trendy framework that makes everything super easy. You can't really afford the overhead that software running on a modern desktop can, so it will require a bit more work.

For reference, the original iPhone CPU was a single ARM11 core clocked at 412 MHz. Obviously it's possible, this Allwinner chip would run circles around that.