Running ERC20 contract on RSK
So, this smart contract, with its setup today, would it be possible to make it use the RSK network instead of Ethereum?

Yes. https://developers.rsk.co/tutorials/ethereum-devs/port-ethereum-dapps/
RSK Bridge can also be helpful for users to swap tokens: https://developers.rsk.co/tools/tokenbridge/

If yes, what could be the pros/cons (eg. cheaper/faster transactions) and whether it would make sense to do the transition?

There are lot of differences. You can read this medium post which explains few technical differences and development of Rootstock: https://medium.com/iovlabs-innovation-stories/similarities-and-differences-between-rsk-and-ethereum-e480655eff37
Scaling is the biggest advantage in using a Bitcoin Sidechain for such experiments.
Rootstock resources: https://github.com/john-light/RSK