It'll be more prone to distortion than mild steel of the same thickness. Size/how the top is supported etc all play a role but FWIW when my proper table has been buried under stuff and i've used my mobile table top (1.2ish mm mild steel skinned thick ply) to repair an ally casting it's ended up looking like the himalayas
The trouble with thin tops for welding tables is that the spatter sticks to it really easily. A heavier gauge top has a greater thermal mass so the spatter struggles to bond with it.
I have a sheet of 3mm on top of thin MDF on top of a timber bench. It's all survived a couple of years of learning to weld.
But I wouldn't like to go any thinner for fear of charcoaling the wood of the bench when stuff gets hot.
If it was purpose built, the underlying wood would be steel, or could be a frame rather than solid to keep it cool, but then there would be even more need to stick with 3mm or thicker.
I lift it all off when I want my woodwork bench back.