Yes. You can log in to your Pulse SMS+ account on any device, and it will download the messages synced on our server from your primary device.
It should be noted that this is a feature that comes with your premium subscription or one time (lifetime) membership. Since the subscription allows you to create an account, it will not be possible to apply the backup to an unsubscribed/free user.
Pulse SMS doesn't provide a way to export your backup to any other format. Everything is end-to-end encrypted. There are a number of apps on Google Play that can export all the messages on your device.