I think they will build some effective barrier - but it will be a relative drop in the bucket, just because of the size of the task.
They can (and should) make prioritized local improvements, to the extent they can afford it. They absolutely can make a significant difference locally, where ever they choose.
But the State alone probably could not build out the whole border wall needed, in a decade.
It will be interesting to see which areas they pick to start.
Big Bend State and National Parks, Eagle Pass, Del Rio, Matamoros to the Gulf of Mexico (Lower Rio Grande Valley NWR) and go both directions at the same time.