no.
as a blacksmith and general metalworking fiend...I've known people that have died from zinc fumes.
Zinc starts offgassing from the steel at about 600F, well within the range of what you'd get on burner contact, especially at the temps you need to et your chips/sawdust/etc to smoke.
Zinc Oxide isn't JUST harmful when inhaled. Depositing a layer of it on whatever you're smoking is still going to give you metal poisoning. Don't risk it to save a few bucks.
Get a stainless steel bowl, or even go to a yard sale and pick up an old cast iron skillet, even if it's a tetch cracked.
as far as I personally am concerned, all galvanized stuff is the work of pure evil.
I can, under NO circumstances, recommend the use of galvanized ANYTHING in a smoker.
Just ask the question 'is it worth me, my significant other, my kids, or my family (except maybe the mother in law) being exceptionally ill, or dying, because of trying to save a few bucks?'
I'm sure people will call down thunder on me for being 'needlessly dire', and perhaps the loss of my acquaintance has something to do with it, but to me, it's a no-brainer.
Get something else. It's really that simple.