Yes. You only need to unlock your bootloader if you are flashing a factory image. If your device has remained completely stock and you are looking to just sideload the OTA, you do not need to unlock your bootloader. Below is a summary of the steps. But it's user beware. I can't be held responsible if anything messes up.
1. Download and install Android SDK.
2. Download and install the add-ons from the SDK Manager which installs things like platform-tools.
3. Enable developer options on your Nexus 6 and enable USB Debugging.
4. Connect your Nexus 6 to your Mac via USB.
5. Open terminal and navigate to the platform-tools folder within the SDK's directory.
6. Run ./adb devices and check whether your device is showing up. You may need to authorize your device within the popup on your Nexus 6.
7. If it showed up, run ./adb reboot bootloader. This will boot your device into the bootloader.
8. Use the arrow keys to select Recovery Mode and hit the power button to confirm.
9. After you see the Android on screen with a red exclamation point, hold the power button and hit the volume up button. This should bring you into Recovery Mode. You'll see yellow text at the bottom of your screen.
10. At this point, your Mac may not see the device anymore. So just in case, unplug your USB cable and plug it right back in.
11. If you downloaded the OTA ZIP into your platform-tools folder, use ./adb sideload "name of ZIP file" to push the ZIP to your device and install. If you downloaded the OTA ZIP somewhere else, either move it to platform-tools and use the previously mentioned command or use ./adb sideload "full path of ZIP file" to push the ZIP to your device and install.
12. After completion, you should be given the option to reboot your device. After rebooting, verify that the OTA installed through the Status screen in your settings. Assuming the correct version is reported, you should be all set.