Not generally, no, that form is not generally used. To minimise an adjective when using "as possible", you need to move the words around:
I use make-up to look ugly as little as possible.
That then has a slightly different meaning, however. It tends to point to looking ugly as little of the time as possible. However, there are alternatives.
I use make-up to look less ugly.
That definitely means you are reducing the ugliness, but it doesn't include the "as possible" element.
I use make up so I don't look any uglier than I have to.
This is wordier, but it indicates the minimisation and uses standard, conventional grammar and word choice. It is natural and idiomatic and conveys all the meaning that you want. However, it does have a fairly strong sense of considering oneself ugly and, probably, resenting that. You could choose a less emotive word to reduce that factor:
I use make up so I don't look any worse than I have to.