Is it possible to use a control scheme with a delay as prefilter? I am studying control systems, and in my studies I have encountered the topic of control scheme of the form 



and I have seen thaht this control scheme is really useful since it is possible to add a lag or lead compensator outside the closed loop, so it won't give stability problems.

At this point I was curious to know a little more and in particular I would like to know if it is possible to use a prefilter which  is a delay. In such a way it would be possible to avoid the problem of stability given by a system with delay.

So, to explain better, I would have for example:

$T(s)=e^{-s}\frac{C(s)P(s)}{1+C(s)P(s)}$

and so I could design a stable closed loop without delay, and then filter the reference with a delay, so use:

$C_r(s)=e^{-s}$

instead of using a closed loop with delay, which gives stability problems.

Do you think it would be a good idea?  Or it would be impossible or conceptually wrong?
1 - It can be a good idea to put a filter $C_r(s)$ in order to smooth the reference. For example, if you have a speed regulator, and the reference jumps from 100 km/h to 200 km/h, having a low-pass filter will smooth the actual reference fed to the closed-loop. It could prevent excitation of unmodeled dynamics, actuator wind-up, etc. That being said if $C_r(s)$ is a simple delay, it has no purposes as far as I can see.

2 - $C_r(s)$ only affects the reference fed to the closed-loop. It will not affect stability of the closed-loop like you mentioned. It also has no effect on disturbance rejection or errors due to modelization (such as unmodeled dynamics).