But will it?

In the UK 2x4, 2x2 etc is still commonly available, but it's 50x100mm. Probably has been for 30 years but only sold as 50x100 for ten or less. Metricating timber was easy because no one's going to notice or care if they get 25mm instead of each inch.

Metals, fastenings, pipes etc converted much slower because metric was often incompatible sizes without adapters.

> Which actually measures 1-1/2" by 3-1/2",

Isn't that because it's 2x4 before planing. cut lumber would be actually 2x4.