Not always.
USAirways learned that the hard way with PSA; in the end, they lost a whole lot on the deal. Same for AA and AirCal. No merger has boosted revenue on a particular route for more than a few months; only until some new competitor stepped in, and fares fell again. And looking at the mainland-Hawaii market, don't you think that there's already a lot of competetors ready to keep fares low?
The question is not "Will people stop flying because of the name on the side of the plane," but rather it comes down to "Will we make more money by buying this other airline?" If you look at the surface and say, "Hawaiian is making money, lets buy them," then sure, it's a slam-dunk. But the problem is that if you buy them, they aren't Hawaiian any more! What makes the airline profitable is lost, then you're stuck with another anchor on the bottom line.
What does Hawaiian bring to Delta that they can't get cheaper on their own? Planes? Nope. Routes? Except for a single daily flight to HND, nothing they couldn't do on their own right now. Employees? If Delta wants to expand, their new-hires will cost them a lot less then the 'legacy' employees that Hawaiian would add.
Hawaiian's profit comes from its own business model. If Delta buys them, the model is broken, and the profits go away, making the deal a bad one.
So tell me again, from a business perspective, why would Delta buy Hawaiian?
HAL