Serious question: Jarvan/Amumu support?

As in, could they work?

passive is great for initiating them 2v2s. Armor shred q and attack speed steroid e for your ADC to go to town. W should give you a fair amount of tankiness. QE combo for some tasty hard CC (even if it's typically going to be once per fight), huge gap closer/maker, and ult is good for some serious lockdown. Does he work here? Is he not able to function with such low income?

should theoretically work with an AP bot, something like which I'm seeing a lot of. Q to initiate, passive for increased magic damage? Ult hits hard and is good too. But while I feel like Amumu's passive could REALLY help out an AP bot lane, is it even worth it to bring him? Does his passive + q and ult justify bringing him or is that not enough to work with the low income?

Thanks!

Note: I've had AP carries in bot with me numerous times and it's always worked out, but in those matchups I always went with Alistar.