Dear Prabhu, 

This year all the states are taking admission in BAMS through NEET score and NEET merit list, on directions of Ministry of AYUSH which were released in 2017. Now, coming to whether or not you can take admission on a payment or management seat in BAMS if you are not eligible or in other words haven't qualified NEET 2018 exam, then, unfortunately, you cannot. 

On May 11, 2018, the Ministry of AYUSH, GoI, clarified to the states that qualifying criteria for BAMS and other AYUSH courses will remain the same as that of NEET, which means that not only NEET ranks and scores will be taken in account while admission, but also its qualifying criteria or cutoff marks. 

Now, unless a state isn't taking admission in BAMS through NEET, you cannot take admission on the same without having qualified the exam. This year all states with exception of Tamil Nadu (as asserted by media reports) will be taking admission to AYUSH courses through NEET. 

Hope it answers.

Good Luck!