For the word on its own? Absolutely. Even in the bible we find instances of variations of להחזיק used in the meaning "to strengthen" (as seen in Nehemiah 3, for

For the word on its own? Absolutely. Even in the bible we find instances of variations of להחזיק used in the meaning "to strengthen" (as seen in Nehemiah 3, for example). In this specific instance, however, it's used as part of a well known phrase throughout the Talmudic and the later rabbinical literature (whose source is from Ezekiel, as noam_k helpfully noted).