Makes sense. In the Flashpoint Universe where Dr. Thomas Wayne became Batman, he started being Batman less than a year after Bruce's death.
If you just want to see Thomas Wayne Batman, skip to 8:07.
I imagine if Alfred took up "the mission" he would not rely on theatricality as much as Bruce or Thomas did. Alfred is more subtle in personality. MI6 likes to be subtle. He might wear a costume just in case he's spotted but Bat-Alfred would probably avoid being seen altogether and his costume would be more subtle than any other version of Batman seen. Also, even a younger Alfred would still be older than Bruce Wayne Batman so he'd probably be less willing to get in direct fisticuffs.
I would have few if any costumed villains but a lot more mobster type villains. Maybe I would add a side plot where Alfred is left the Wayne estate but there is a highly corrupt member on the board of Wayne Enterprises that is trying to seize the company from him. Overtime this corrupt corporate officer becomes deeper and deeper entrenched with the criminal element until he essentially becomes a super villain. Maybe give this villain a last name in common with one of Batman's traditional foes (Nigma, Friez, Krane, Napier, Cobblepot, Kyle, Eisley, Quinnzel, etc.)
He'd probably kill really bad people assassin style. If they weren't really bad, he'd probably knock criminals unconscious and leave them at police stations with a pile of incriminating evidence.
Hypothetically, if I was writing a Bat-Alfred comic. This would go on for a while before Bat-Alfred realizes the criminals he's not killing are being let go scot-free. Alfred would have a moral crisis of whether he should let execute the petty criminals or not. After some soul searching Alfred than uses his espionage skills to purge Gotham PD and the judiciary of the corrupt individuals that let criminals go free.
Any Gotham without Bruce Wayne in it should be crappier than regular Gotham, so this is probably a physic victory. The power vacuum in Gotham PD may lead to fewer blatantly corrupt cops but the police are undermanned and underfunded so crime doesn't really get any better. I may or may not have James Gordon die here for shock value.
After decades of fighting crime from the shadows, Alfred is beginning to slow down from age and is losing hope. I would end the comic with Alfred adopting a young idealistic orphan named Dick Grayson. Possibly adopting an orphaned Barbara Gordon too or maybe just becoming her mentor. Thus implying that Alfred could have some young proteges to continue the fight.
