Is there any possibility of slow rising hCG up to 6 week becoming normal afterwards and deliver a healthy baby??

Yes. it is possible and not rare that a slow rising HCG and then normalization of the HCG may result in a normal fetus and delivery and child.
Beta HCG. The beta hcg is a measure of whether the embryo is progressing properly. Regardless of the levels of hcg, if the pregnancy progresses, than there will be a healthy baby ( as least as far as hcg is concerned). I hope this answers your question. Thanks for using Healthtap. :)