It takes 30-40 seconds to boot up my Erisin ES9405EU and it starts playing automatically providing you've set up the options to do so - this is what it does on mine as Poweramp starts playing tracks stored on my microSD card automatically for me. I don't know about the radio as I never use that.
I don't hear anything before then it's booted up.
I have the power options configured to leave the stereo in sleep mode for 30 minutes when I leave the car so if I pop to the shops, the stereo starts working quite quickly when I return to the car instead of waiting 30-40 seconds again. Once the 30 minutes are up, it powers itself down and you have to wait for the stereo to fully boot up again. I've never had any battery issues with this, and I've not updated my Gateway either.
Hope this helps?