Thanks for your interest in Connections! Connections and cMap are designed to be as plug and play. For most users it gets no more complicated that playing with the large number of shortcode options that cMap enables to tweak it.
I’m not entirely certain I understand this, “Our site utilizes and iframe or other imbed code from the map provided but there could be a conflict if Connections uses WordPress users.“. I can say that Connections does not use WordPress users. The only area Connections does use users is with the Link extension for Connections and even then it only sets a user meta ID which is a behind the scenes/never seen thing that is used to link a Connections entry to a user.
I hope that answers your question thoroughly!