Yes! Rambl integrates with Salesforce and HubSpot so you can log the call directly from the call detail screen in either the mobile or web app.
* IMPORTANT: To access Salesforce from Rambl, you are required to have the Web Services API add-on, which is included in Enterprise and Unlimited Editions. This add-on is available for Professional Edition for an additional fee per license. Contact your Salesforce AE for details.
No. Since Rambl is designed to work only with calls, it's only "listening" when you place a call via the Rambl app or when you receive an incoming call to your Rambl number.