Can Vagrant point to a directory of Puppet manifests for execution?

Firstly, do I understand the "new" (non-import) way of calling multiple manifests correctly, in that a directory is to be pointed to in which all the *.pp files inside it will be executed?

Yes, you do. See here:

If you’re using the main manifest heavily instead of relying on an ENC, consider changing the manifest setting to $confdir/manifests. This lets you split up your top-level code into multiple files while avoiding the import keyword.

Moreover, manifest and modulepath are also getting deprecated in favor of directory environments and the manifest directory behavior, see here:

Now that directory environments are completed, config-file environments are deprecated. Defining environment blocks in puppet.conf will cause a deprecation warning, as will any use of the modulepath, manifest, and config_version settings in puppet.conf.

This is a pretty big change for a lot of deployments, but should be a good improvement in the long run.

And secondly, has Vagrant "caught up" with this new change to accommodate the referencing of directories in conjunction with Puppet's deprecation of "import"?

No, it has not; from their docs:

manifest_file (string) - The name of the manifest file that will serve as the entrypoint for the Puppet run. This manifest file is expected to exist in the configured manifests_path

For use with Vagrant, you're stuck with dealing with deprecation warnings for now, which is unfortunate. But, import's not slated for removal until 4.x, so this gives Vagrant some time to catch up.