I haven't tried this solution, infact i don't even own a PS4 but i am a PC Enthusiast but it should definitely improve noise. Those external cooler solutions are there to improve heat transfer away from the heat producing components, so your microchip (-> Processor) and also have an overall higher thermal capacity through more metal.
Furthermore, a larger fan can be attached to greatly improve the air that passes through the cooler and therefore increase cooling capacity of the device. This could not only lead to lower noise but also potentially higher performance because the chip stays cooler allowing it to draw more power (another whole topic but generally the more cool the more faster). Be aware tho that not every fan is the same so you could get some noisy fan that really sucks if you cheaped out but it will almost certainly be better than the standard cooling solution.
Assuming you dont know much about physically modding a PS4 or building PCs this may be a very risky operation to make and just some simple dusting of your PS4 could do wonders.
Side Note: Good Fans to suggest here would come from companies such as "Noctua" (eventho they have some ugly turd and tan coloured fans they are by far the best performing) or "beQuiet!".