There is a difference between whether it might “work” in a pinch and whether you should do it at all. Technically, you can weld on just about anything. However, you risk lighting it on fire, or at the very least damaging it.
Generally, it would be a very, very bad idea to put a piece of metal on a wood surface and weld on it. That’s a recipe for starting a fire and would not be safe in any way. So NO, it won’t work as (A) welding table if we assume that one of the main functions of a welding table is to keep you safe.
If budget is a serious issue, you’re better off buying a super cheap welding surface from Amazon, Harbor Freight, or Northern Tool. Please do not weld on wood.