Nope. You should have been backing up before you had it shattered.
With luck you may have had Google Photos turned on, so you may want to check it out on a web browser. If you don't then you need to replace the phone screen yourself so that it won't be formatted. It's standard protocol for repair centers to format the device.
There are multiple ways to automatically back up photos, Google themselves will do it so I would check your Google account as chanchan05 suggested.
If the phone has been connected to the computer before it might work, but by default these phones are set up to prevent data being read and taken off by a comouter, usually need to toggle a setting on after plugging in. Its worth a shot but odds are nothing will happen.
There's also an SD Card slot, did you have one in the phone? If one was in it should have been saving the photos to that, in which case you just pull that out and put it into another phone, tablet, or computer.