"I hate running."
I guess the copula is needed because 嫌い is a na-adjective. Na-adjectives in predicative position (in position of the verb) need the copula afaik, so you would at least have to use the plain copula だ (or it would probably sound very, very casual in the sense of rejecting, like someone in English just answering "Hate it!" when asked).
Short answer: yes, it's possible.
Long answer: there are many rules surrounding nominalizers こと and の.
の is used when nominalizing clauses dealing with immediate time and/or location. In these cases, only の is allowed:
1) When clauses deal with senses: 誰かが叫ぶのが聞こえた。
2) When second clause occurs at the same time as the first one: これを運ぶのを手伝ってください。
3) When the second clause has a verb dealing with stopping of cancellation of something: お酒を飲むのをやめましょう。
こと typically deals with more abstract, distant concepts. Cases when only こと is allowed:
1) When the following clause deals with internal thought or communication: 明日の授業に出られないことを先生に伝えてください。
2) When you are nominalizing a single sentence (=the following clause is です/だ/である) - a.k.a. "N1は/が N2だ" pattern: 私の趣味は走ることです。
3) Set phrases and grammatical constructions such as ～ことができる, ～ことにする, etc., always take こと.
All other cases, including 好き / きらい, can have either.