AROTC branching is based on: 1) needs of the Army and 2) OML. Do well in ROTC, maintain good GPA, rock the APFT and there is a decent chance to branch Corps of Engineers. The Army commissions more officers from ROTC than USMA or OCS so there will be slots to fill. Probably half of my Engineer Basic Course were ROTC grads (active duty, guard, and reserve)
I spent my career as an Army Engineer officer, the US Army Corps of Engineers (USACE) is comprised of both the Engineer Regiment (the uniformed component) and the public engineering component also called USACE or COE as Jcc123 mentions. Both components are commanded by a single, dual-hatted 3-star general and fall under the Army and DoD. What makes the COE unique and likened to a federal agency is it's civil works mission which is generally funded directly through Appropriations from Congress and sometimes single line item appropriations from the President's budget and are separate from the DoD's budget for military construction on military bases worldwide.
Engineer Districts (within COE/public works side) are commanded by Engineer Officers and have military personnel assigned as staff and project managers. COE also contains the 249th Prime Power Battalion, a troop-unit specially trained and equipped to provide rapid power generation and supply in national emergencies.
A newly commissioned officer will serve their first several tours with troop units within the Regiment. There is a chance here to serve in construction units that do construction and have design teams within them but the type of engineering work performed is small scale as it is based on wartime construction which is temporary in nature, although there are opportunities to perform work on military installations. I had the chance to build steel barracks buildings, forward landing strips, and small structures stateside and build roads, bridges, a medical clinic and other structures overseas. Just don't expect to be a hard-core design engineer in troop units. More like a construction manager. After the advanced course and generally company command, there are opportunities for Advanced Civil Schooling and to branch out with a chance to serve in the COE as a project manager or at one of the research centers or labs as an engineer. One of my classmates is the Chief of the Army Structures lab. Another ROTC friend went on to be a nuclear type scientist with the Army. There are plenty of opportunities to be a "real" engineer or earn a PE license if one puts the effort forward.
I will agree though, having worked with USAF (Prime Beef/Red Horse) and USN (Sea Bees) engineers, that they are much smaller in size and tend to "nuture" them more with a higher percentage of them having licenses....generally because they have more chances/likelihood of working in Public Works organizations and get much more exposure to the skills and projects more likened to what a civil engineer does.
Long post but happy to chat via PM if you want/need more info. I have served in tactical units and USACE so have seen both sides of the fence.