Most CD players spit out 2Vrms full scale. In my opinion that is way too high. Why? Well, most power amps reach full power usually around 1V. Very few require up to 2V. The point is, a signal straight out of a CD player will drive virtually any amplifier into clipping. Hence, the linestage acts as nothing more than an attenuator. Worse yet, active linestages have 15dB to 20dB gain. The result is a LOT of attenuation. One step forward, two back. Why all the gain? So you can throw it away!
Simpler is better. Sonically you will get the most musical and transparent results at minimal gain. This is even better if you can bypass the volume control (minimal attenuation). Basically, try to throw away as little signal as you can get away with. Otherwise you are adding more distortion and coloration than is needed.
To answer your question, yes, a PICCOLO will add some front end gain to increase the signal level. So you can throw it away later. However, this will tend to drive the input of the CORNET2 too hard on transients leading to possible harshness. The CORNET2 phono is designed to sing with nominal cartridge levels of 5mV (and their expected +20dB peaks), not 20mV. The significantly higher levels drives the second stage tube out of its linear operating region (only on transients), leading to distortion.
The other possibility is to use a PICCOLO on the output of the CORNET2. Yes, it can handle pretty high signals and will spit out 2Vrms. But again the levels are too high. In this case limited by power supply rails. A step-up transformer might work better here. Just make sure it can handle the relatively high signal levels.
Perhaps your best choice is to decrease the output from the CD player. You will then apply your linestage in a more linear fashion, leading to better sound.
jh