you didnt really mention what type of competitve trail. That's a broad term, if you are talking long distance race type rides, no way, wrong breed wrong build. I wish someone had told me the facts of life before I bought my current horse. I wouldnt consider a QH, just not going to do well long term and why set yourself and your horse up for marginal at best results ? If your OWNED that horse already and wanted to do it Id say sure get it in shape, go for it, have fun , concentrate on completions, but no way I would intentionally go out and BUY a horse like that. Look for something at least half arabian with big feet and strong cannon bones.
Now if you are talking competitive trail like ACTHA ? Where the focus is cowboy challenges and obstacles ? Well that horse may be ideal for stuff like that.