Statement of purpose: How to state PI backup
Let's just clear the situation within the scope of two cases:


The Pl-based universities: In this case, acquisition of a positive response from a Pl would pave your way, considerably. Within this scenario, you are supposed to mention your propensity toward the target Pl within SoP. Then, your SoP will be analyzed and sent to that fellow, has which been named within that SoP. Here is the very step, within which the Pl could admit you.

You better to pay close attention to two important points: 
interpretation of the Pl's tone within the response is, merely, up to yourself... For example, he/she might say that: "You look a qualified applicant, I will encourage you to apply"..., but the other one's reply might be: "Your CV sounds considerably overlapping with my current projects. Would you please take some explanation into account regarding your programming skills, as most the current projects are highly-simulated-based ones...". One could claim that the second answer might be more promising than the first one, but the others may take both energizing and apply into both... So, you need to apply for the replies, are which stemmed from serious propensity of the corresponding Pls. Hence, you must cite the desired Pl's name within the application.
The admission-committee-based universities: In this case, the Pl's reply just could be effective to find your turning point. Actually, their positive opinion could be compiled as your gratifying situation in comparison with the typical admitted students to the program. In contrast, the deferring answers should warn you about the high risk of the taking application into account. Therefore, mentioning the Pl's names in this scenario is not useful, noticeably.