@itisyeetimetoday yes, you can do that, although you'll probably end up creating more error than you expect. The results will likely be good enough for a school report, but not for anything that would actually fly.

It's important to stress that $C_L$ is by no means a driving factor in aircraft design. You're generally more concerned with range or endurance and the lift to drag ratio, which $C_L$ can be helpful in determining.

@AirCraftLover It depends on what you're trying to accomplish. If you have an idea for an aircraft and nothing more, then no, you can't use that formula to find $C_L$. You can get a rough estimate by taking the section lift coefficient $C_l$ of the airfoil and reducing it slightly to account for lift loss from wingtip vortices, but that doesn't take into account contributions or losses from the fuselage, horizontal tail, etc. Before completing an aircraft design, you'd want to have built multiple models and tested them in a wind tunnel, where you could find $C_L$.

@AirCraftLover sorry it took me a while to get back to this. You can certainly write the equation that way to solve for $C_L$ if you're taking measurements of the lift (i.e. you know $L$, probably in a wind tunnel) but if both $C_L$ and $L$ are unknown, you can't solve for both in a single equation. In that case, you would likely have to use CFD.

@Derrick You're looking for the Reynolds number with regard to scaling. If you're interested in designing a model aircraft that will fly, you should get an introductory textbook for aerodynamics. You can change any property of the wing, but it will have other effects besides just increasing lift.

@CarlWitthoft Yes, Peter's answer does still apply, I only wanted to point out that one doesn't need to generate/have "tables of engine data" (i.e. more than one set of numbers) to employ the rubber engine concept. Additionally, single parameters can be modified without having "all other parameters change accordingly." While scaling the other parameters might be a good idea, ultimately it's up to the designer to keep the engine specifications reasonable. Peter's answer is correct, but in my opinion might convey too strict of a definition of what the rubber engine concept is intended to be.