Not OP but I can definitely say that's a yes from me after doing this repeatedly. I cold email people once a month or so, and if it is to do with anything sensitive I'll check to see if a public key is available for them (on their website is best, else I check a public key server and use that key as long as there is only one listed).
I get a better response rate from PGP/GPG users too, I can only recall one not responding to an encrypted message and I sent a follow-up message unencrypted which they responded to.
I think it's important to send PGP messages for ordinary communications whenever possible, because this normalizes it and may increase the workload for those trying to defeat it.
Honestly, I wouldn't focus on (3), because as I see it, if you can replicate the feel of email, things like (1)-(2), so that it can replace email in contexts without (3), then (3) will just come naturally as it slowly replaces email.
Edit: All this is assuming it isn't tied to a phone number or something similar, of course!
The "Web of Trust"  fills that role:
> As time goes on, you will accumulate keys from other people that you may want to designate as trusted introducers. Everyone else will each choose their own trusted introducers. And everyone will gradually accumulate and distribute with their key a collection of certifying signatures from other people, with the expectation that anyone receiving it will trust at least one or two of the signatures. This will cause the emergence of a decentralized fault-tolerant web of confidence for all public keys.