I am trained in both as a doctor. Are you talking about working independently or as part of the multidisciplinary team?
If you have good prior understanding of neurodevelopmental conditions, you could potentially do ADOS training (companies like hogrefe do it), but you wouldn't be immediately ready to just do it. You would have to have a period of supervised training and assessing with an experienced person observing you. When you first start it's actually really hard to simultaneously administer the ADOS and also observe all you need to see. This means it's always better to have someone observing you for a bit. They can point out any administration difficulties and also observe the child's behaviours.
However, ADOS is only part of the assessment. You also need someone to do a full autism specific history ( you can learn to do this using structured interview tools such as the disco or 3 Di) and you need to be able to review all the other information and make a decision. From my perspective in order to be able to do this latter part, you need really good knowledge and experience in all the differential diagnoses such as trauma, attachment, learning difficulties, other neuro diversity and underlying chromosome and genetic differences. For my money, this part is best done by a psychologist or a doctor (paediatrician or psychiatrist).
As for ADHD, the assessment is basically the latter part with observation of behaviour. Again there are some structured interviews that you can learn for history taking (eg DIVA). There are plenty of people out there doing these assessments using these tools but again I feel you need the background knowledge and experience in other conditions and so I personally feel a psychologist or doctor is best placed. Having said that these assessments are now often done by clinical nurse specialists.
My personal opinion is you could absolutely do training and be a great part of the MDT and work privately for a separate organisation, however, I think you would struggle to practice completely independently as cases often need other members of the team (speech and language, doctor, psychology, psychiatry etc).
Private occupational Therapy is in high demand though and you certainly could do more independent practice in doing movement ABC assessments for developmental coordination disorder (although still need a doctor for criteria c and d) or sensory needs assessment.