I would like to bring my boat home this weekend – from a Marine to do some work to it. My drive way is a 15-degree slope or so and am concerned about the boat rolling or trying to roll once I unhook it. I have some wheel chucks but do not have 100% faith they will not just slide on the driveway.

My question I would like some guidance with is can I lock the surge break on the coupler to keep the trailer brakes on while in place and the trailer unhooked? If so how?

Honestly, you are setting yourself up for failure... I would not tempt it just for the simple fact if, if, they gave way, what would be in your path, and who could it hurt? Just chock those puppies up real good and you should be fine...

Let the tounge all the way down and make sure it doesn't rain.

I was going to Chock them and then do the brake as a back up. I would rather it be as secure as possible.

I would put good chocks under all 6 tires. Then you should have a safety cable attached to the coupler so if it ever came unhooked the brakes would apply. You should be able to pull that arm up and then I would fasten it up so it can't go back down.
Then you should run a chain from the back of the trailer into the house and wrap it around your bed post so you will know when it rolls out into the street.

Tall chocks are step one.

Then you can use a ratchet strap, and wrap it around the front of your coupler (sideways, around the ball coupler lip), and around some part behind your trailer tongue, perhaps where it splits to out to the beams, or the winch stand. Put the ratchet on the side away from anything delicate (wires/brake likes), and tighten it. It will cinch the surge brake actuator in, and "set" the brakes.

However, you want your primary holding power to be the chocks.

Change over to electric over hydrolics and when you disconnect wouldn't the breaks lock up?

No. They're not like air brakes. E/H uses an electric pump to power the brakes. You'd have to run the pump all the time to get brakes.

Good aircraft-quality rubber ribbed chocks can be had at Mcmaster-Carr. If they can hold a jet aircraft during a full-power maintenance run, they'll hold your boat. Chock all four on a two-axle trailer. It's probably not necessary to do all six if you have a 3 axle unless you just plain can't sleep at night.

As suggested, hook the cable on the surge emergency lever to something solid just in case the dog chews your chocks up.....

be carefull not to start the motors with the bow down, don't want any water reversion issues.