Yes, you can do Deathbringer on 10-heroic and then ZONE OUT and switch to 25-man normal.
Warning: In situations like the one you've described, the game will sometimes automatically force you to zone back in on 10-man or 10-man heroic. If this happens, there's a very simple fix: Invite another person to the group and make it an official raid group. Be zoned out and set the raid to 25-man and it should stick. This doesn't always happen, but I have had it happen to me before.
And a general overview of how raid lockouts currently work: Once you kill a boss on heroic mode, you are locked to that raid size for heroic bosses. You can, however, switch between 10 and 25-man for NORMAL modes, but doing so requires zoning out first.
I'm curious: Why are you interested in 25-man normal, but not 25-man heroic? Are you farming gear or shards? If you're farming shards, then 25-man heroic, assuming you can kill the bosses, is vastly superior. I'm guessing you need heroic 10-man Deathbringer for achievements or a piece of gear, in which case there's no getting around it... but I figured I'd ask.