No, the DAG files are too big for 4GB cards. I would not recommend buying new mining hardware as Ethereum is moving to POS, so I would recommend staking instead.
If Ethereum failed to switch to pos the next cards that will be like rx580 4GB are those with 6GB memory like the 1660s 2060 6GB etc but with lolminer they will have some extra month after 6GB DAG is over, I don't know how lolminer devs manage to pull this stunt, they did a very good job.