Women who use a lighter screening process typically focus on the quality of a client's references, or, in some rare cases, having multiple whitelists (or the equivalent on other platforms).  
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The specific email address used in those cases rarely plays a factor, in my experience, provided she can verify the client's trustworthiness to her satisfaction. If the references rave and the email and cell match, they are generally good to go, regardless of the type of email given.  
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Those who conduct more thorough screening, however, often typically demand a work email address and/or an email associated with the client's public identity as part of their verification process.
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But you are so correct, as every provider is different, and thus not part of some monolithic group, as there is never one set way every girl handles these situations. Some women will even change up what they need on a case by case basis.
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The women who make me nervous are the ones who will lessen their normal process when times are tough, which obviously increases risk. Every women in this lifetstyle who confided in me they got busted, stated they did so when they let their guard down and didnt do their typical, in depth research on the guy, or in some cases, none at all. ugh.
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But as you (plural) know, not doing your due diligence can lead to worse outcomes than just getting busted, sadly.

The question is what does a woman do with the phone number to screen?  

 
If it's just to check blacklists and such, then it shouldn't matter what kind of phone it is.  

 
If it's used to run a check through a service then that's flawed. Many people, myself included, have had their personal info scrubbed from the online world. When I plug my number into one of these services nothing comes back.  

 
In addition lots of people nowadays use MVNOs as phone service providers and some, if not all, are prepaid so there's no contract and no personal info needs to be provided so they can put any name they choose on the account, or none at all.