Here's the problem with using Inbox/Gmail (same thing) with Hub. The default "delete" action on the hub does not archive mails, it actually puts them in the trash. This is actually the correct expected behavior of IMAP, but it's not what most Gmail user intend. When we get rid of an email, we archive it, so it's searcheable years later. In order to do that with the hub, you need to move the email to the "All Mail" folder, which can actually be set up as a two step shortcut. it's not bad. The other disadvantage is that the search function in the hub only searches email in the synced folders, and it does not search the server like the gmail app does. So, sadly, as much as I like the hub, I manage my gmail through the gmail app.
I use the Inbox app for managing mail, but have the same account configured in Hub (with notifications disabled) for the timeline. That works fine for me.