"I believe I may not have to undergo any immigration checks as I will be a transit passenger" - you WILL, because you are arriving from outside Schengen (Pier B) and transferring to a Schengen flight (Pier A) and must go through passport control between the two for entry to the Schengen zone - and again when you get to Frankfurt as you will be transferring there from Schengen to non-Schengen, and so exiting the Schengen zone! Only if you had been transferring from a non-Schengen to non-Schengen flight directly at BRU would you have avoided this, as a transit passenger.
In addition, you go through security checks for ALL flights, irrespective of whether you came in on another flight or checked in in Brussels. And the fast track lane is not open to all business-class passengers, only certain airlines, e.g. SN.
If you booked both flights (ORD-BRU and BRU-FRA) through United, on the same ticket, and they told you this was a legal connection, at least they will take responsibility for rebooking you if you miss your flight to FRA. If you booked these tickets separately, on the other hand, you're on your own.