Is jayce a viable carry in low elo?

Literally every champion can carry in low Elo. No exceptions.

The real question is: can you play Jayce well enough to carry out of your current Elo?

I would most definitely say yes. He is an excellent duelist, sieger, and split-pusher. Just focus on grabbing all them sweet objectives and you'll be swimming in LP.

He's great in high elo. Very good laning. Can poke well and do good burst damage to squishies. Most vulnerable when out of position around heavy CC champs.

Jayce is great in all Elo, primarily as a counter to Riven and other all-in bruisers (little known fact, Jayce plays golf on a daily basis). Great in team comps that lack poke (for example, your mid is Panth, who has a short poke on his Q, but not far enough to trade without getting poked back). Only thing you'll need to know mainly is when to switch between Cannon and MC Hammer stance (Ctrl+3 Ctrl+3 Ctrl+3 huehuehue) during lane, team fights, etc. Commonly it would be swapping from Cannon to Hammer to disengage or regain mana from his passives.

The real question is : "Are you good with X champion ?"

If the answer is yes, then keep playing him. Eventually you'll carry some games either by yourself, either you'll get out of there because you are not at your deserved elo.

Follow up question here:

Can Jayce carry games where bot lane isnt doing too well, or is outright feeding?

(Reason im asking this is that from what ive noticed from my recent low elo games is that either one bot or the other just dominates)