I purchased a Hamax child seat (not unlike this one), but when attaching it to the frame the child seat is too low and is touching the rear wheel.
As you can see in the photo, I don't think I can secure it higher up in the frame.
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I would strongly recommend against it. I have a similarly designed seat from Yepp, and the amount of force exerted on the frame is substantial. Seat posts can shear, and would result in a bad time for everyone.
You will also find that having your child that high up lightens the steering a lot. Mine is install in the correct position, and I have to consciously shift forward to maintain firm wheel placement; putting in on the seat post would make this even worse.
There are some that are designed to clip to the seat post, but their design is very different: This one for example and they rest on a pre-fitted rack.
Have you considered a crossbar seat instead?
Answering your question - perhaps the seat stem will hold both you and the child and the child seat all together. And maybe not - depends on the total weight of yourself, the child and the seat. Should it fail, not only you're putting your child in danger but also your ability to have another children (black humor). Furthermore, by putting the centre of weight higher, cornering will become more difficult, again putting yourself and the passenger in danger. Bottom line - I wouldn't do it.
Taking this answer a step further, I see the following solutions to your problem, provided you want to keep the seat and the bicycle: