Yes, it is very likely that it will work with your L brackets.
Most L-Brackets have a cut-out area around the connectors, so you still have access to the sockets.
On Nikons Pro DSLRs, the Unleashed N1 is attached to the front of the camera (round 10 pin port) so it’s out of the L-Brackets way anyway. If there isn’t a cutout for the cable that you need for some Nikon cases, most L-Brackets have a slot rather than a hole for the tripod mount screw. This means you can shift the L-bracket a little bit and make space for the cable. You would only need the USB socket on the side.
Regarding Canon it’s the same case. Most of the time the brackets have a cutout for the sockets. This means it would work as the Unleashed for Canon, so the Unleashed C1 and C2 needs the HDMI and USB socket.
These are the measurements of the new Unleashed:
C1, C2: 13.8 mm x 5.5 mm (10 mm with plug casing) x 35.2 mm
N1, N2: 13.8 mm x 5.2 mm (7 mm with plug casing) x 16.1 mm
C1, C2: 0.543in x 0.217in (0.394in with plug casing) x 1.386in
N1, N2: 0.543in x 0.205in (0.276in with plug casing) x 0.634in