Technically it is possible, it is just not very convenient. You are not shut out of any component of RoM as a free-to-play player but the amount of time and repetitive tasks, as well as the gulf between the pay-to-win and the free-to-play players, can be daunting.
Any class, not just tanking, at end-game level as
a totally free-to-play would take a lot of hours to farm the gold necessary to get the equipment you need. The gear upgrades could be obtained by trading in-game gold to players who will purchase the items from item shop for you. (But you will also need to find trust-able players and always take screen shots/video of your business transactions). With the current in-game mechanics, tanks must have
Hatred Runes at end game. After that, the other gear and stats you need can also be purchased from the Auction House. But all in all, it is a lot of gold and therefore a lot of hours. Maybe 4-7hrs a day, depending on how familiar you are with the game, what level you are, and how helpful your guild is and how helpful you are to your guild.
However, that is if you are planning on end-game tanking at lvl 72 with Chapter 4 stats and lvl 65+ gear. Below end-game level it is much more possible. Gearing up for level 55-65 instances is much more attainable and they are the stepping stones to end-game anyway.
Moreover you said
mostly free to play. If you stuck to spending say $10-20 monthly, saved up, bought diamonds and gear upgrades on sale, grinded the mini games regularly for stats... it is much more possible. Still quite a few hours of game play though, maybe averaging 2-3 every day, but not as much as totally free to play yet you won't get to end-game as fast as someone who easily drops $75 a month or who throws down $300 at a time for upgrades.
Note: once you get to end-game it is easier to make the gold back, since you will be the one selling end-game stats and equipment.
