Could I mine bitcoin and profit?

With a 970, you're not going to profit a lot. You might barely just pay back for electricity. WIth some underclocking and/or picking a currency that's new and easy to mine with a good future ahead of it is probably your best bet.
Look around at new smaller mineable currencies and pick something that you think will grow.
That's what I did and I managed to turn around a huge profit from it, though this was back in the day when Bitcoin was around $4,000, and still on the rise.