Welcome!
First, let's take a deep breath, and look objectively at your reasons for suspecting that there is a plan to remove your child from this school. Has anything been said to indicate that they view him as a disciplinary problem? Does the school have support staff to do skill-building in areas like self-regulation of attention and behavior?
It is entirely possible that the school genuinely views this as a problem-solving attempt, not as documentation for excluding a student. I've worked in public schools, and consulted to privates, and the vast majority of these observations actually are to see if there are strategies that can be offered to the classroom teacher. (Certainly, all of mine have been.)
Second, if we can separate the presenting behaviors from the question of ulterior motives of the school, it does appear that there are behaviors worth investigating. I understand the reluctance to label, especially very young (and I share it, despite working in a label-heavy profession), but the label is much less important than access to appropriate interventions is. In special education (aka IEPs, which are usually relevant only in public schools) and health insurance coverage, the label of ADD/ADHD affects access. Elsewhere, it doesn't really.
One of the differences though, that I should mention, is that it sounds like he may have started speech therapy through EI (early intervention) or an IFSP, which is under different rules. If he received those services through the public schools' preschool services (after age 3), on an IEP, then he already has a label of sorts. If he is being serviced through the private school he attends, then that would suggest that the school has some investment in serving students with needs, and may have the resources to support the classroom teacher with additional strategies.
In any case, there is rarely anything additional at risk, and often something to be gained, from having a third party observe the interactions between your child and his instructional environment.
Third, you have mentioned his strengths in oral language and reading, and possibly in mathematics, but not whether the teacher is modifying instruction to present challenge appropriate to his zone of proximal development. Instructional mismatch is a key contributor to off-task behavior and inattention in a classroom environment. It may be that a thoughtful and respectful question to raise with the observer when the observation has been completed would be how his behavior varies or remains the same depending on the task or circumstances, including the level of challenge of the academics.
