Hey there! That should not cause a problem as in upward facing dog majorly the upper back where there is kyphosis as mentioned by you would be getting the appropriate treatment considering it a postural kyphosis.
Do perform yoga asanas if there does not seem any problem or hindrance doing them.( no pain )
Extension exercises will help hunchback and anterior tilt be helped with pelvic tilt exercise, hip flexor stretch exercise.
While doing yoga, do not go for holding the position as that has little chances of causing trouble. Probably as mentioned by you do not lift the pelvis...just arch backwards.
Next Steps
it would be better to visit a physiotherapist and get your exercise plan.
Health Tips
try not to be sedentary. Keep moving and keeping the posture accurate consciously.