Yes. The MLA allows contractions in its publications. In professional scholarly writing, sometimes a formal tone is desired, but often a more conversational approach is taken. When overused, contractions can be distracting. But there is nothing inherently incorrect about contractions, which often keep prose from being stilted and make it more approachable and easier to read. However, clarity and context matter.
Contractions may not be suitable for all types of formal writing—like a research paper, where protocols for formal writing are being learned. After all, it’s easier to understand when to bend a rule once it has been mastered. There are countless other examples of formal writing when contractions would be unsuitable (e.g., if you are writing a judge requesting leniency in sentencing, contractions will seem dismissive).
When to avoid contractions in your prose:
If the contraction could have more than one meaning: she’d can mean she had or she would. If a contraction results in lack of clarity, avoid it.
If more than one word is contracted—for example, he’d’ve for he would have.
If have is pronounced “of” when elided: could’ve (could have). The consensus is to avoid such formulations in formal writing (Garner; O’Conner).
If the contraction can be mistaken for a possessive, even momentarily: The teacher’s key to the classroom and can’t be replaced (better: The teacher is key to the classroom and can’t be replaced).
Garner, Bryan A. Garner’s Modern American Usage. Oxford UP, 2009.
O’Conner, Patricia T. Woe Is I: The Grammarphobe’s Guide to Better English in Plain English. E-book, Riverhead Books, 2009.