will a piece of 2" x 3" tube steel with 1/4" thick walls support the front of a counter top that is 24" deep by 108" long, with total weight of top, substrate lavatory bowls, etc., of 250lbs?
Securely mounted at the ends of the beam, and with the countertop well supported along the rest of the perimeter, yes.
Do you want to use this steel as a horizontal beam supporting the front edge of the counter? Or do you want to use it as a vertical column? Or are you using it as a cantilever to support the counter with the steel attached to the back wall? What is supporting the steel?
In general, this steel should be able to do any of that, but it’s hard to say without knowing more details.