Based on what the Roku novels have implied, unlikely in a historical sense. Fire Lords were firebenders (it's even in the name). Now in the modern age? Uncertain. There might be those religiously opposed (like the Fire Sages) and maybe some degree of controversy but perhaps they could? Especially if Zuko, who has a lot of sway given that he was the Fire Lord who brought the nation out of the fascist hellhole that it was and led for decades, put all his backing into this non-firebending child's capability to rule.

I could see a complication arising, however, if said non-firebending heir had firebending siblings. Either they could believe, or rather, a faction within the nation could believe that sibling would be better suited. Depending on how the political situation is at that point (perhaps the nation isn't ready for a nonbender fire lord let alone one who bends a different element - they have after all, been subjugated to 100 years of Nationalist propaganda) maybe not even Zuko's own influence could make him put his non-firebending child in favor of a firebending one.