It would NOT be safet to assume that EAB aircraft cannot operate in Class B airspace, because it's incorrect. There are no restrictions on the type of airspace into which EAB aircraft can fly, assuming that they're properly equipped to fly in that airspace.
There's one more thing to keep in mind when you're operating in Class B airspace: in general, you need to be at least a private pilot to enter the airspace. Student, sport and recreational pilots can enter specific Class B airspaces, but only after they receive training and an endorsement from an instructor.
VFR aircraft must obtain an ATC clearance to operate in Class B airspace.
SVFR operations may be authorized for aircraft operating in or transiting a Class B, Class C, Class D, or Class E surface area when the primary airport is reporting VFR but the pilot advises that basic VFR cannot be maintained.
However, if you wish to operate in class A, B, or C airspace, or at an altitude of over 10,000' MSL, or within a 30 nautical mile radius of the primary airport in class B airspace, you will need a transponder and altitude encoder (commonly referred to as mode C).
The upper limit of the airspace should not exceed 10,000 feet MSL. However, high airport field elevation, adjacent high terrain, or operational factors may warrant a ceiling above 10,000 feet MSL.
You may fly without ADSB under the Class B or Class C shelf provided you remain outside of any Mode C veil. §91.225 tells you where you cannot fly. It says you cannot fly within the lateral boundaries of the Class B or C airspace or above the airspace.