Yes. Your son will learn English quickly- young minds do and the younger the better. You don't say where you're moving or which of Switzerland's languages is yours - there are such things here as French language immersion schools though they're private, not public, and only found in larger cities.
And there are schools more used to just this situation than others - some cities here are used to having children come into their schools speaking languages other than English. But in any school, your young son will hear English spoken and learn English from that and quickly.
Welcome to the States!

Hello. I concur with Lockmama; many public schools offer ESL programs. Your son will probably pick up English in a very short amount of time. Since you already communicate well in it, I would even encourage you to begin to speak to him in it now...you might try to read simple English language books to him, and perhaps put little labels on common items around the house, such as "bed" or "chair" or "table" or "pencil" to help familiarize him with those words. All the best in your relocation!

Many American schools have an ESL (English as a Second Language) program. Check with the schools in the area you will be moving to. Good luck to you in your move!