Is there a downside to upgrading to RoS asap

Unless you actually looking to create those Hellfire rings, upgrading would stop and prevent you from completing those rings. There are also skill updates and gear changes would would normally break your current build. So if you want that Level 60 ring set, I would hold off on adding the expansion to your b.net account till you are finished with your rings.

Unless you actually want a level 60 hellfire ring that badly, get the materials for it without RoS since you will be 60 and won't level up. Once you got RoS and level 61, level 60 hellfire ring's materials will be out of reach since you'll start getting level 70 hellfire ring's materials instead. If you have the materials for the level 60 and got RoS, you can still craft it if you start a level 60 game.

Same goes with the legendary drop from bosses, once you get 61, Diablo won't have a 100% legend drop as it will be moved to Mathael instead. Easier to do that without RoS then once all your characters have got their legendary, upgrade to RoS and level them up to get the legendary from Mathael.

Overall, I think upgrading is worth it. Troyen's answer might be the sole good reason to stay without RoS but, imo, it ain't worth it. The experience gained from doing all there is to do in RoS, the drop rates from rifts and greater rifts will be worth more than the time spend/wasted (depending how you see it) at 60 trying to get a hellfire ring that you will most probably end up not using.