The answer is yes, but it depends on the person, and the situation. People studying Shakespeare must in fact use his quotes. Many people use Shakespearean quotations without knowing that they are in fact from Shakespeare. Often people know them in inaccurate forms.
Example, "all that glitters is not gold" (original in Merchant of Venice "all that glisters is not gold"
"there's method in his madness" (original in Hamlet "though this be madness, yet there is method in't")
"gilding the lily" (original in King John "to gild refined gold, to paint the lily")