The answer is yes and no.
To simplify things only a bit, "yes, we can" is not a literal translation of sí, se puede. In fact, there is no good literal (that is, word for word) translation of the phrase. Sí clearly means "yes," but se puede is problematic. "It can" comes close to its literal meaning but leaves out the vague sense of emphasis and/or completion that se provides.
So just what does se puede mean? Out of context, I'd probably translate it loosely as "it can be done." But context matters, and as part of a group chant the translation of "yes, we can" is entirely appropriate. Se puede is a phrase of empowerment (puede is a close cousin of el poder, a noun meaning "power"), and "we can" conveys that thought well.
Want to know more? Check out these lessons:
- Principles of Translation
- Introducing Se
- Using Se as the Equivalent of the English Passive Voice
- Using the Spanish Verb Poder
- Conjugation of Poder