Greg
If I'm following you correctly, you seem to be suggesting the use of a single Paypal transaction in order to establish the identity of investors in the proposed private fund, and that you intend this to be some kind of nominal fee with the substantive transactions taking place in Bitcoin later on?
If so then, in and of itself, that sounds fine (I am not so attached to my pseudonymity as others here, I suppose), but would you not then need to link the Paypal account to a Bitcoin wallet? A signed message on the blockchain could be used to establish the link in one direction, but how would you corroborate it on the Paypal side? And are you quite sure that Paypal's KYC/AML is something you want to count on? There have been some troubling accounts of Paypal freezing completely legitimate Kickstarter accounts in the name of anti-fraud/AML. That could be a problem if the kind of activity you're proposing were construed as crowd-funding by Paypal. Beyond that, Paypal may not necessarily be sufficiently compliant with UK law and might, in fact, add additional regulatory exposure as you'll be accepting 'real money' as part of the setup of the fund.
To answer your primary question though, the idea of using Paypal for ID verification doesn't strike me as a deal-breaker persay. I certainly find it far more palatable than turning over copies of my passport, credit card and driver's licence to WeExchange (A totally outrageous suggestion, in my books. That's more than enough information to facilitate identity theft). But I'd like to hear more about how you envision the logistics of this working.