This comes up in advertising all the time - you can increase how many impressions an ad gets easily by just showing it more but the conversion rate depends entirely on the kind of user, match between user & ad than anything else.
In this case, the people who paid for the app self-selected themselves by the act of paying, but the barrier to install the free version is much lower than that.
You have to consider:
1. The number of users that would never pay for your app, but are happy to download it for free.
2. The number of users that would never pay for your app without trying the free part first.
3. The number of users that would pay for your app without trying it for free.
You then have to consider the amount of revenue you lose from Type 3 to support Types 1 and 2. Hopefully you come out ahead, but you may not.
In this case, the people who paid for the app self-selected themselves by the act of paying, but the barrier to install the free version is much lower than that.