Control and transfer functions
Your initial 4 transfer functions look correct (assuming the stated inverses exist). Then, if you are using scalar transfer functions,

$$\hat{y}(t)=\hat{u}(t)P=P\hat{u}(t),$$

though the second notation is more popular. So we have

$$\frac{\hat{y}}{\hat{u}}=P.$$

Then you can derive T1 as

$$T_1 = \frac{\hat{y}}{\hat{d}}=\frac{\hat{y}}{\hat{u}}\frac{\hat{u}}{\hat{d}}=P(1+CP)^{-1}$$

and do the same for T2:

$$T_2 = \frac{\hat{y}}{\hat{r}}=\frac{\hat{y}}{\hat{u}}\frac{\hat{u}}{\hat{r}}=PC(1+PC)^{-1}.$$

So, the answer to your question is yes, you can. The answer in the non-scalar case is actually also yes, but at the condition that you pay attention to inverses (they must exist) and to the notation you use. As for instance

$$\hat{y}(t)=P\hat{u}(t)\neq\hat{u}(t)P,$$

and

$$C(1+PC)^{-1}\neq C(1+CP)^{-1}.$$

Note that you wrote both in your question. If you were treating a non-scalar problem, you should also use I to define the identity matrix.