Yes, interest and sustainability can co-exist in the long run. Interest has already survived for millennia, so it's probably one of the best-tested sustainable mechanisms we have as a civilisation.
And interest does not require perpetual exponential growth, neither for savings nor for debt. We've had plenty of periods of history where we haven't had exponential economic growth, and we have had interest.
Money and resources are different things
Don't confuse money with resources: they are exchangeable, at always-varying rates, but they are not the same thing. Money can be created at the push of a Central Banker's button - that's what Quantitative Easing is. And debt / savings can be eliminated at the push of a button too - that's what debt cancellation is. And both of these things are happening around us right now.
Interest is a real price, in a real market
Furthermore, interest represents a real price - the price of credit. If you've got a sum of money that you can access now, you can choose to spend it now, or you can choose to spend it later. If you've got the same sum of money, but you can only access it in one year's time, then you can spend it any time after 1 year, but at no point between now and then. So, by definition, that money that is locked away for a year is worth less than money available now, because you can do less with it. And the price of that is what interest represents - the price of credit.
Credit has a real price, and to hide that real price, would distort the market for credit, creating long-term distortions, and actually worsening economic efficiency and thus economic sustainability. Now, economic sustainability is by no means the only kind - there's social sustainability, resource sustainability, and so on. And they are all important.