Sure, I can see that turning into a product, although similar systems already exist. (e.g.: google alerts, zapier, etc)
Make sure you connect with as many 3rd parties as you can for notifications besides email. SMS, Zapier, slack, customizable webhooks, etc.
In the long run maybe connect to api X and automatically post some replies or follow some rules to execute some task or mark some potential lead with some tag, etc..
Just my $0.02 knowing very little about the subject and just reading the idea as is. But do run some research on competitors before spending too much time or money on it, because I'm sure there must be some heavy duty players in similar fields, which at the end of the day is probably closely related to lead generation and marketing automation tools.