You can play PvP and get fairly high up without spending money, but it takes time and grinding. There is strategy to what you are doing, but you are limited with low level equipment.
Basically, PvP runs in plateaus. You’ll slowly rise, but eventually you’ll run up against Tommus, Regenerate, Dominate, Knockback, or what have you. You won’t be able to do much of anything against these until you you get them yourself. So you may well stall out in a band of say 1200 to 1500 (just chose that at random), but until you get the ability to cast Regenerate you’re going to be stuck in that band. Once you get that ability though you may well go up 400 points or so until you hit a new plateau. Even once you have it the problem is you don’t always get that character in your line up, and if your opponent does you are back at a disadvantage. I think I am finally at the cusp of topping my final plateau, but to do it I need to get several legendary items so I will usually go into battle with at least one character with an instakill attack. Since I am strictly F2P that might not happen for a while, but I am solidly in the top tier level so it doesn’t really matter because my awards won’t get any better anyways.
The other thing is there seems to be some sort of strategy that has emerged since I got into the higher levels of PvP of people not leveling to try to get easier opponents. I tend to think character level is a small part of the matchmaking algorithm, but you could still within a narrow band run up against people who have an artificially low level so to speak. Similarly, you could be facing P2W guys who just dropped $2000 when they downloaded the game, and now they are moving up the ranks. Also if you are near the time where you will go up a dungeon level you end up fighting people who just moved up to the new dungeon, got beat three or four times in a row by teams that were overpowered compared to them, and so drop back down a dungeon level and beat up on teams that they are overpowered against.
So can F2P reach the top level of PvP? Yes, at least for now, but it takes time.