You can define it to be anything you want, so it's theoretically possible, but pretty pointless; the usefulness of the coefficients is in comparing the efficiency of different wing DESIGN FEATURES - by a more representative non-dimensionalisation, you can eliminate the influence of purely area changes and compare, say, the effect of sweep, or t/c, on the lift.
Knowing that a wing that is the same design but twice the size generates twice the lift isn't really insightful. Knowing that a change in t/c by 1% changed the CL by 3% for two DIFFERENT SIZED wings allows you to understand the influence of t/c on CL.