I'm an advisory teacher for Looked After Children, and although the issues LAC face are different to adopted children, they are not completely dissimilar. I am often confronted with "He just needs former boundaries", erroneous reward charts, exclusions "So-and-so has had a bad life, and SHE doesn't do that" etc.... There is a serious lack of information out there.
IME, schools on the whole are really welcoming of training on the issues LAC and adopted children face, but that this is often better presented as a strategy meeting focusing on a particular child, their strengths and needs and what approached can be effective. This can then be further developed into more general training which puts the issues into a wider context.
I think your idea of approaching the school is an excellent one. In school training works best when it is compulsory, so I would suggest approaching the head or Designated Teacher for LAC and scheduling a session for a lunch time with food provided as a sweetener. Teachers have very full timetables, so may sometimes be resentful of having to attend. Trying to make the pressure on their time constraints minimal at first will be worth it in the long run, as it will open up a dialogue.
I would also see if there is a Virtual School or LAC education team in your LA, and contact them directly to see if they offer training to Designated Teachers- we do, and teachers have been given time off from school to attend. We have had very good feedback, and the knowledge imparted has improved the outcomes for many children.
Lastly, I would speak to the head about the Pupil Premium Plus which will be given to children adopted from public care from April. The school needs to be thinking NOW how they will spend the money to improve the academic outcomes for specific children. Tis could be a good way to introduce the discussion. Some of the money could even be used to send teachers on specific external training courses.