Yes, you can do it.
However, I wouldn't recommend it for new characters (specifically, new players). The newer you are, the more limited you options. Furthermore, at this stage, you'll want to explore and try out several things that are not very efficient, using an ISK/h metric. Things such as highsec exploration sites.
Keep in mind that you will also want to have surplus ISK to enjoy the game and PLEXes can be a big ISK sink.
My recommendation is: close the client, figure out what you can do, sort by ISK/h and then calculate how much you'd need to play to cover the subscription costs. Then decide if that's acceptable, or even fun.
After all, instead of grinding for hours each day, it is likely that you could use that time to earn money on the side and then pay the accounts and possibly even trade for ISK.
Remember that PLEX prices fluctuate by market supply and demand. Currently they are approaching 500M.