Source XLR to Balanced Preamp will increase gain?

^^ No. It depends on how the output of the CDP is set up.

If balanced but not differential, then you will see double the voltage. But if the output is differential and floating (for example, if an output transformer is used in the CDP), it may be set up so that the voltage from pin 2 to pin 3 of the XLR is the same thing as what is seen across the RCA jack.

So you will want to check with the manufacturer on this one.

Milpai, the adaptor will not cause the circuit to be balanced. It simply allows you to hook things up.

Differential is where the circuit has an output based on the difference between two inputs, inverting and non-inverting.

'Floating' is where the output is independent of ground. Usually though it is referenced to ground in some way, although there is no signal current associated with the ground connection. You have a balanced TVC if I understand correctly; it should be capable of operating this way as all audio transformers can.

'Balanced' is two identical circuits but with opposite phases, inverted and non-inverted. How this **might** be different from differential is that it may not automatically convert a single-ended input to balanced, and it may not always produce one output from the difference of the two inputs.

IOW it is possible to have a balanced and differential circuit, and also one that is merely balanced but not differential. In terms of noise and performance, it is far more likely that the balanced differential circuit will perform better, and even better yet if it is floating.