OK yes it is possible.
I am running Android 7.0 and just bought a HTC Bolt from Sprint.
To set an alarm sound for alarms, you go to the main settings gear icon > Sound & Notification > Alarm. This alarm will set the default sound for all alarms in the clock app. I'm saying this because it's a bit weird to then set the sound for the timer.
To set the sound for the timer:
1. Bring up the Clock app
2. Tap on the TIMER tab, if it is not already the active tab. On my device, a green line appears underneath it.
3. Tap on the three vertical dots above the TIMER tab
4. Tap on Alarm sound. I know. It sounds like you'll be changing the sound for the alarm but it doesn't. It only changes the sound for the timer "alarm" sound! Nice one coders!
5. Select the sound you want from the list of sounds
6. Tap APPLY at the bottom of the screen
This is easily immediately testable. Tell google to set an alarm for 3 minutes. Then tell google to set a one minute timer. You'll see it worked.
As far as setting your own sound, that's another issue that I'm sure you can resolve!