You may certainly grill or smoke on all hardwood coals. It is a dollar thing for me.
@MoDoug
I have an offset smoker for wild caught salmon, and I just burn alder in it. When I need alder I call my friend at DOT to ask what intersections they have complaints on that are low on the list. He says "go to the corner of blah and blah". I fill my truck with alder, clear the sightlines of the intersection back to DOT regs and he sends a chipper truck a few days later for what I leave behind. Alder is literally a weed up here, but salmon smoked on alder, like beer, is proof God loves us and wants us to be happy.
When I am near Austin, TX they burn all oak in their offset smokers for beef, but they would have to pay for alder what I have to pay for white oak. Flat sawn white oak is $10 per board foot up here, wider than 8", figured, or quartersawn starts at 11.50/bf and goes up quickly. Texas beef smoked on Texas oak, more proof of God's love.
When I am doing beef on white oak I put paper in the bottom of the chimney, then a couple or three inches of charcoal, and then 4 or 5 fist sized chunks of white oak. Light that off, let the white oak burn down to coals(20-40 minutes, yelow flames OK, you want the blue flames burnt out), fill the chimney with more charcoal, let that get going pretty OK, and then pile all that mess on one side of the grate to get your reverse sear going. Once your steaks are up around 110-115 dF IT on the indirect side bring them over to the hot side, directly over the coals, to get a nice crust on them, stick them in the cambro ardound 125-127dF IT and put on some clean underwear so your wife doesn't get distracted after dinner.
If you got white oak coming out your ears, just use that and don't stretch it with charcoal. If you are using 1/3 glowing alder coals and 2/3 charcoal your salmon will be within a couple whiskers of mine. Smoldering hardwood chunks is a gateway drug to real (red hot glowing coals) BBQ I think.