Secondary school in the US just for one month

I am in the process of planning 1 or 2 month long visit to the USA, with my children presumably on J-2 visas. One of the still open questions is, should my children attend a secondary school while there. (Let's assume Denver, CO, as a location, although I prefer answers aimed to tackle the general question, or backed with experience from cities in general.)

How much of a problem is incurred to the school by a pupil who attends for much less than a full school year? (I am thinking about various practical and regulatory effects of varying class size. It would also be problematic to visit the school long before actually starting attendance if the school required that.)

What's the minimum standard of fluency in English for (briefly) attending a secondary school in the US? My children can read and understand English on a basic level, but it's likely that they'll struggle with the spoken language more than with anything else throughout the whole stay. I view that as a good thing and as an opportunity to complement their current "academic" and "gaming" experience of the language with a little exposure to spoken, real life use of the language and of the culture.

Should the potential language barrier factor affect how we search for a suitable school? I am NOT looking for instruction in a foreign (that is, non-English) language, nor for ESL education. I am rather trying to consider factors like public vs. private school, educational system of the school, cultural diversity of the neighborhood, distance from a university campus and so on.