Yes, all Z-Wave generations are backwards- and forwards-compatible (though, of course, you'd run into possible problems in the reverse of your situation where a device supports a new "command class" for a feature you need and you're using an older controller that doesn't support it--but even then you'll still get basic control or reporting).
Note that, depending on how old your switches are, they may not report physical status changes (one made on the device itself as opposed to on the hub) back to the hub on their own. This is due to a patent, now expired, that most manufacturers did not license. To work around this, you could set up the Z-Wave Poller app on Hubitat or use some other solution that achieves the same goal (less is generally better with polling). Or you could only use the hub for changes. You could also replace the devices, as many have done by now. But there shouldn't be any reason you need to.
You will need to migrate your devices manually; the only hope, which worked to some extent on older hubs, would be to add it as a secondary controller, but that does not work on current hardware and software.