For now, you can, but we discourage using Inbox to manage your personal business email account right now. Here's why.
We built LeadSimple's Inbox to be a hub for shared customer communications to eliminate the silos that are created when teams use their personal business email accounts to email customers. The reality is that personal business email accounts are private by nature and this creates all kinds of problems if they are used for customer communications:
Customer-facing emails are hidden from everyone on the team, making collaboration more difficult; you have to constantly forward emails, and CC team mates to facilitate collaboration.
Your customer experience suffers. If a team member is out sick or on vacation, their emails with customers will likely sit for days without a response because no one else on the team knows they exist so they can't reply to them.
Managers can't see the emails that are being received or sent and have no way to measure the effectiveness of their support, coach their team, or improve their customer communications.
Shared inboxes are an efficient, scaleable way to manage customer communications that eliminates the bottlenecks that are created when the whole team uses their personal business emails to communicate with customers.
Our recommendation is to use LeadSimple's Inbox to manage your shared inboxes, and continue managing your personal business email account in the system where it is hosted (i.e. Gmail, Outlook, etc...).