Yes. My horse once had a foot like that and did endurance just fine. Often horses with club feet are not noticeably lame. You only will notice when the foot is corrected that they are much more sound, and things you thought were unrelated such as difficulty picking up that lead or leaning in when cantering on that club side go away. However, the kindest thing for your horse is to correct the club foot.
This foot used to look just like yours. That was until I did a lot of research on club feet and found out how to correct them. It often does not work when people try to fix these for several reasons. First, the bars are jammed up inside the foot as in this picture:
If you took your horse's frog off, this is what you would see. Bars growing up inside. This makes it painful for the horse to stand on the foot, so you can't just trim the hoof wall down around the heels. You have to trim the bars every two weeks (sometimes slightly below the sole level) and slowly let them grow out from inside the hoof. The frog grows up tall and skinny and needs trimming down as the heels come down also.
The sole compacts in the heels clear down to the ground also, so it looks "live" and like you can't take it out. Those tall bars hold it in like a vise. But you have to slowly take the foot down about every two weeks by trimming a little bit of sole out with the heel wall and bars (about 1/4 inch at a time).
Because the heel has been so long, the horse will have weaker muscles on the back of the leg (the ones that push the heel down). So the lowering has to be done gradually to let those muscles gain strength and stretch as the heel comes down. It would be like if you wore high heels for a year every day and then went barefoot. Your calf muscle would have shortened, and it would hurt to walk flat on the ground until that muscle stretched out again.
Finally, you can read all about the properties of tendons online if you are concerned about the Deep Digital Flexor Tendon being "contracted." Don't read farrier sites, read medical sites and you will discover that this is a myth. Tendons cannot contract, they can only stretch (1-2 inches) and cutting the check ligament is a short cut to waiting for the muscles in the legs to gradually strengthen and lower the heel rather than causing it to drop because the ligament was cut.