No, I don't think bbq ashes are good, especially if from briquettes.

Using just charcoal from wood, I grew a Better Boy tomato in 50% compost/50% charcoal and it was dwarfed compared to those in compost alone.

I kept a small fire pit in my front yard and occassionally I would burn good wood and then dig out the ashes and dirt and either spread it or add it to a compost pile. I thik it helps and whatever I plant over the old pit area seems to thrive better than the same plants nearby. Right now I have 20 or so stalks of corn and the ones that grew in the firepit area are a foot or more taller than the ones nearby. Higher than an elephants eye my mid July.