Question about Sony Alpha 6000

Short answer: no. Explanation: Sony has 2 mount systems, A-mount (e.g. on the a37, a58, a68, a77 etc.) and E-mount for mirrorless cameras (e.g. a6000, a6300 a-7 etc.). Without an adapter, you cannot use an A-mount lens on an E-mount; first of all, this has nothing to do with the mechanical elements, but with the distance to the sensor: with the E-mount, the flange focal length is much shorter, so it has to be "artificially" lengthened for an A-mount lens with an adapter. The Sigma zoom you are talking about has an A-mount, so it won't go on the a6000 without an adapter (regardless of image quality). There are two adapters: E/A-3 and E/A-4. The first has mainly manual focus adjustment (although also AF, but completely unusable because of the slowness), the second has AF. I have tried different zoom combinations: normally the AF works quite well (tested with Tamron 17-50 and Sigma 18-35 1.8 Art). My problem with the Sigma is that the factory settings for the AF areas are very problematic: this ranges from front focus to back focus. There is a (quite cheap) docking station that allows you to set this individually to a particular camera (e.g. the A77), but it remains a tedious fiddle. However, once the AF on my Sigma 18-35 is right, the quality is sensational.
In combination with a Sony a6000, you would have to see how the Sigma 17-70 behaves. But as I said, it won't work without an adapter anyway. I can, however, recommend the 3 fixed focal lengths from Sigma for E-mount: 19 mm, 30 mm and 60 mm; very cheap and very good. In terms of optical quality, the 60 mm is so excellent that it is actually a waste of money in relation to the price.