Glad to see this question & the answers. My ODD is in a similar boat- she just turned 6 and has done gymnastics since 3.5, and she is not particularly coordinated or athletic- though she's not bad necessarily. I don't know, I'm not a coach!
My ODD is in the pre-pre-team class (anyone can sign up for the beginner class at our gym, if they are the right age) and so far hasn't been kicked out (after 1.5 years of not moving up) so I assume that she's doing OK enough. I have overheard other parents being told that "the rec classes here are really great, your child would probably like that better" so I know it happens. I do see a lot of improvement, and hope that she gets moved up soon (to the next level of pre-pre-team, no illusions of grandeur here) because she's aging out of her level. I am guessing if she isn't ready to move on soon she will be recommended to go over to rec- would not be the end of the world, they even have intramural teams in rec and she would probably enjoy that. She does want to do team, but I wonder if she REALLY wants to do JO or if she would be happy in any sort of team environment- her motivation to me seems mostly social. In any case, for the moment it's all working out, so we just keep going.
FWIW they don't spend much time on cartwheels in the pre-pre-team classes at our gym. My guess is that the time is too valuable, so they do a lot more conditioning & flexibility & body shaping. They have introduced cartwheels and my DD loves to practice them wherever she goes- she finally gets the idea (it happened in the last few months) and she can do a real cartwheel but with ridiculously bent legs. I don't worry about it!
They do work on pullovers & drills in her class, and she still needs help getting over, but she's looking better than she used to. Her class only meets once per week for an hour, the next class is twice per week which I believe would make a huge difference- that's partly why I hope she moves up! The other reason is that her little sister is almost certainly moving up to her current class in the next session.. that is if she doesn't demand to switch to another activity (I just posted about this). YDD is a lot more athletically gifted and she has coaches drooling over her all the time- she is almost 4. Part of the reason why I know ODD is just OK is that the coaches don't get all excited about he the way they do with YDD, and I have seen it when kids in her class get that kind of attention. But ODD has some very good qualities- she is friendly and enthusiastic about everything, everyone appreciates her good attitude. And she has a pretty decent work ethic, if she lacks focus at times. She also has lots of fears but with the right guidance she works through them. Part of why I keep her in the team track as opposed to rec is that they are really trying to get her to do stuff she doesn't think she can do. I think it's great for her, wherever it leads.
So as for the OP's question, I think that yes, it's probably possible, if your daughter wants it and works for it. That is the assumption I'm going on with my kid. It might take a while- my daughter is on the slow track and I am fine with that.