Are you thinking of staying at a "tent only campground" at times? Or just want more options for finding a last minute one-night campsite at a standard campground?
Generally speaking, many tent only sites are set up where you park in a parking lot and then walk a short distance to the campsites. In these areas, you will probably not be OK with camping there as you will technically be camping in the parking lot (and there won't be any extra space between vehicles). For a quick overnight, you might be OK depending on the host.
For those with their own parking pads, often the "livable" area of the campsite (where you can set up chairs, campfire, etc.) is often set apart from the pad either by a short climb or hike. Again, for a quick overnight stay, you probably will be OK. For longer stays, it may not be that conducive to camping out of an RV (you'll be making that short climb/hike every time you want something - versus tent camping where it's all up there).
As for technical rules, it depends on the campground and the other campers. In a tent only campground, you are much more likely to get called out on it. In a combined campground, it will more likely depend on your neighbor tent campers - if you annoy them, they will complain and you'll be asked to move/leave; if you play by their rules, they will leave you be.
I have a 21ft C and I camp a lot at public campgrounds (FS, COE, etc.). I can honestly say that I haven't seen a tent-only site that I would have preferred over a general site. I can fit into the smallest of the general sites (tent or RV) and have always found one with a great view, privacy from other campers, etc. While I can fit into the tent only sites, they never offer anything better than the other sites and often offer less (no views of the water, etc.).