Good question, let's see... 
Let me preface this with a bunch of caveats: Dapr has been around for a while but I've never really dug deep into it. I think there's actually a lot of platforms we can either integrate with or make use of and make them have a "Swift native" distributed actor user experience. There's also Kalix ("Akka serverless") which is another runtime like this.
Can we do "virtual actors" with Swift's distributed actors?
Yes!
Our distributed actor design is very much so prepared to handle the virtual actor pattern; we "just" need the runtime impls to catch up a bit with the language 
For example, you'll notice (quote from the docs you linked):
Each such actor is uniquely identified by an actor ID.
That's why distributed actors have the Self.ID which is managed by the actor system
This is a common trait for all distributed actor runtimes, from Akka, Orleans and all the way to OTP and Dapr and others.
In general, you should probably start with:
as it explains the concept pretty well. And please note that the pattern originally comes from Orleans, so more docs for inspiration are available here:
I'd also give Kalix a look, since Akka's "cluster sharding + persistence" is exactly the same as the virtual actors pattern in practice, and Kalix is the serverless offering.
I think it might be much easier to get a Swift SDK going for Kalix and we'd then be able to write both servers and clients using DA... (supported languages https://docs.kalix.io/reference/supported-languages.html )
Sidenote: Pure Swift
We could also implement a pure-swift solution for virtual actors based on the cluster library: GitHub - apple/swift-distributed-actors: Peer-to-peer cluster implementation for Swift Distributed Actors
I'm in the middle of updating it to the latest toolchains as we're preparing for WWDC, so within a few weeks one could start playing around with implementing Virtual Actors for the cluster. It'd mean you can "host" virtual actors with a very minimal deployment. Though of course the above mentioned managed runtimes are also interesting.
We could also look at extending the Swift AWS Lambda runtime:
to be able to "host" virtual distributed actors...
So yeah, lots of work ahead of us and we'll need to figure out as a community which runtime is most interesting and try out a few as OSS libs I think 
What about Dapr right now then?
I'll be honest here that it is unlikely that I myself will have the time to look into integrating with Dapr, but I do agree that such integrations is exactly what we should be doing with DA as it gets released with Swift 5.7 
If you'd like to look into it I'm more than happy to offer consultations or something like that to help you write such Swift SDK for it 