I think so, yes; if you say "herb" with a non-silent 'h', you'd write "a herb". By way of example, the name Herb is commonly pronounced with a non-silent H, so

I think so, yes; if you say "herb" with a non-silent 'h', you'd write "a herb". By way of example, the name Herb is commonly pronounced with a non-silent H, so even in a dialect where "herb" is pronounced "erb", you'd write "A Herb picked up an herb.".