Can a handrail with a baluster channel be used with wall brackets?
Yes, that is a Type 1 handrail and is legal if: 1) it’s at least 1 1/4” in diameter and not more than 2”, 2) if it’s not circular, (which yours is not) it must have a perimeter of at least 4” and not more than 6 1/4” and a cross section dimension of 2 1/4”. (See ICC R311.7.7.1)

Type 2 handrails are larger (like made from 2x6 trim) but must have finger grips. (See ICC R311.7.7.3.2)

Make sure there is 1 1/2” clear between the handrail and wall. 

Make sure the handrail “returns” to the wall or extends to the ground or post. That means you need to miter the handrail at a 90 degree angle so it fits tight to the wall. 

Handrails are not required on stairs with 3 risers or less. 

Mount the top of handrail between 34” and 38” above nosing of tread.